/**  / 


COURSE  IN  DESCRIPTIVE  GEOMETRY  AND  STEREOTOMY. 


BY  S.  EDWARD  WARREN,  C.E., 

PROFESSOR    OF    DESCRIPTIVE    GEOMETRY,   ETC.,    IN   THE  RENS- 
SELAER  POLYTECHNIC   INSTITUTE,    TROY,   N.  Y. 

The  following  works,  published  successively  since  1860,  have  been  well  received  by  all  the  sci- 
entific and  literary  periodicals,  and  are  in  use  in  most  of  the  Engineering  and  "Scientific  Schools" 
of  the  country  ;  and  the  elementary  ones  in  many  of  the  Higher  Preparatory  Schools. 

The  Author,  by  his  long  unbroken  connection  with  the  Institute  at  Troy,  has  enjoyed  facilities 
for  the  preparation  of  his  wprks  which  entitle  them  to  a  favorable  consideration. 


I.— ELEMENTARY    WORKS. 

These  are  designed  and  composed  with  great  care ;  primarily  for  the  use  of  all  higher  Public 
and  Private  Schools,  in  training  students  for  subsequent  professional  study  in  the  Engineering  and 
Scientific  Schools;  then,  provisionally,  for  the  use  of  the  latter  institutions,  until  preparatory 
training  shall,  as  is  very  desirable,  more  generally  include  their  use ;  and,  finally,  for  the  self-in- 
struction of  Teachers,  Artisans,  Builders,  etc. 


1.— ELEMENTARY  PLANE 
PROBLEMS.  On  the  Point,  Straight 
Line  and  Circle.  Division  I. — Preliminary 
or  Instrumental  Problems.  Division  II. — 
Geometrical  Problems.  12mo.  cloth §1  25 

2.-DRAFTING  INSTRU- 
MENTS AND  OPERATIONS. 
Division  I.— Instruments  and  Materials. 
Division  II.— Use  of  Drafting  Instruments, 
and  Representation  of  Stone,  Wood,  Iron, 
etc.  Division  III. — Practical  Exercises 
on  Objects  of  Two  Dimensions  (Pavements, 
Masonry  fronts,  etc.)  Division  IV.— Ele- 
mentarv  Esthetics  of  Geometrical  Draw- 
ing. One  vol.  12mo,  cloth 125 

3 ELEMENTARY  PRO- 
JECTION DRAWING.  Third 
edition,  revised  and  enlarged.  In  five  di- 
visions. I. — Projections  of  Solids  and  in- 
tersections. II.— Wood,  Stone,  and  Metal 
details.  III. — Elementary  Shadows  and 
Shading.  IV.— Isometrical  and  Cabinet 


Projections  (Mechanical  Perspective).  V. 
— Elementary  Structures.  This  and  the 
last  volume  are  especially  valuable  to  all 
Mechanical  Artisans,  and  are  particularly 
recommended  for  the  use  of  all  higher  Pub- 
lic and  Private  Schools.  12mo,  cloth 

4.— ELEMENTARY  LINE- 
AR PERSPECTIVE  OF 
FORMS  AND  SHADOW'S. 
With  many  Practical  examples.  This  vol- 
ume is  complete  in  itself,  and  differs  from 
many  other  elementary  works  in  clearly 
demonstrating  the  principles  on  which  the 
practical  rules  of  perspective  are  based, 
without  including  such  complex  problems 
as  are  usually  found  hi  higher  works  on 
perspective.  It  is  designed  especially  for 
Young  Ladies'  Seminaries.  Artists,  Decora- 
tors, and  Schools  of  Design,  as  well  as  for 
the  institutions  above  mentioned.  One 
vol.  12mo,  cloth 


II. -HIGHER    WORKS. 

These  are  designed  principally  for  schools  of  Engineering  and  Architecture,  and  for  the  mem- 
bers generally  of  those  professions ;  and  the  first  three  also  for  all  Colleges  which  give  a  General 
Scientific  Course,  preparatory  to  the  fully  Professional  Study  of  Engineering,  etc. 


I.— GENERAL  PROBLEMS 
OF  ORTHOGRAPHIC  PRO- 
JECTIONS. Being  a  quite  extended 
collection  of  elementary  and  higher  prob- 
lems of  Descriptive  Geometry.  1  vol.  8vo, 

full  cloth,  numerous  large  plates $4  00 

|5^~  A  thoroughly  remodelled  edition  of 
this  work  is  in  preparation. 

II.— GENERAL  PROB- 
LEMS OF  SHADES  AND 
SHADOWS.  Including  a  wide  range 
of  problems,  and  a  thorough  discussion  of 
the  principles  of  shading.  1  vol.  8vo. 
With  numerous  plates,  cloth 3  50 


III.— HIGHER  LINEAR 
PERSPECTIVE.  Containing  a 

perspective  construction ;  a  full  set  of 
standard  problems :  and  a  careful  discus- 
sion of  special  higher  ones.  With  numer- 
ous large  plates.  8  vo,  cloth $400 

IV.— ELEMENTS  OF  MA- 
CHINE CONSTRUCTION 
AND  DRAWING.  Onanewplan, 
and  enriched  by  many  standard  and  novel 
examples  of  present  practice  from  the  best 
sources . .  7  50 


NOTES  ON  POLYTECHNIC  OR  SCIENTIFIC  SCHOOLSinthe 
United  States :  their  nature,  position,  aims,  and  wants.  8vo,  paper,  §0.40. 

Under  this  title  is  presented  a  tabular  view  of  the  existing  scientific  schools  of  the 
United  States,  together  with  many  observations  on  the  organization,  courses  of  study,  and 
administration  of  such  schools ;  besides  their  relations  to  other,  and  especially  preparatory, 
education ;  the  whole  being  of  interest  to  the  many  educators  who  would  modify  existing 
preparatory  schools  to  meet  the  wants  of  the  Engineering  and  other  Scientific  Schools. 


ELEMENTS  OF  MACHINE 

CONSTRUCTION  AND  DRAWING: 


OB, 


MACHINE  DRAWING, 


WITH    SOME    ELEMENTS    OP    DESCRIPTIVE    AND    RATIONAL    CINEMATICS. 


A  Text-book  for  Schools  of  Civil  and  Mechanical  Engineering,  and  for  the  use 
of  Mechanical  Establishments,  Artisans,  and  Inventors. 


CONTAINING  THE  PRINCIPLES  OP  GEARING  ;    SCREW  PROPELLERS  ;    VALVE  MOTIONS,  AND 

GOVERNORS  J    AND  MANY  STANDARD  AND  NOVEL  EXAMPLES,  MOSTLY  TBOM 

PRESENT  AMERICAN  PRACTICE. 


BY 

S.  EDWARD  WARREN,  C.E., 

R  IN  THE  .RENSSELAER   POLYTECHNIC   INSTITUTE,  AND  AUTHOR  OP  A  SERIES 
OP  WORKS  ON   DESCRIPTIVE  GEOMETRY  AND  STEREOTOMY. 


NEW    YORK: 

JOHN  WILEY  &  SON,   PUBLISHERS, 

15  ASTOR  PLACE. 

1872. 


Entered  according  to  Act  of  Congress,  in  the  year  1870,  by 

S.  EDWARD  WARREN,  C.E., 
In  the  Office  of  the  Librarian  of  Congress  at  Washington. 


CONTENTS. 


PAGE 

PREFACE xiii 

SOURCES  OP  MATERIALS,  ETC xvi 

ELEMENTS   OF   MACHINE   CONSTRUCTION  AND  DRAW- 
ING   1 

BOOK  I. 

SIMPLE,  OR  SINGLE  ELEMENTS  OF  MACHINES. 

PART  I. 

Introduction. 

General  principles 1 

Scales 2 

Elements  of  projections 4 

Constructions  of  the  ellipse 10 

Special  definitions 12 

Classification  of  Machines 13 

Functional  classification  of  mechanical  organs 15 

Geometrical  classification  of  mechanical  organs 19 

Reduction  of  scales. . .  .20 


PART  H. 

Theorems,  Problems,  and  Examples  on  Elements  of  Machines. 

CLASS  I.— SUPPORTERS. 

SECTION  I. — LOCAL  SUPPORTERS. 

A— Point  Supporters. 

PiUow  Blocks. 

EXAMPLE  I.— A  heavy  pillow  block 22 

EXAMPLE  II.  —A  Putnam  pillow  block 24 

47.  Heavy  lines. 

EXAMPLE  III.  —A  French  pillow  block 25 


CONTENTS. 


EXAMPLE  IV.— A  locomotive  main  axle  box 26 

48.  Shaft  hangers. 

EXAMPLE  V.— A  bracket  hanger 28 

EXAMPLE  VI.— A  self-oiling  drop  hanger 29 

EXAMPLE  VII.— Turbine  and  spindle  footsteps 30 

49.  Cold  rolled  shafting. 

B — Line  Supporters. 

EXAMPLE  VIII. — Locomotive  guide  bars  and  cross  head. 31 

50 — Progressive  forms  of  cross  heads. 

O— Surface   Supporters. 

a — Plane  Supporters. 

b — Developable  Supporters. 

EXAMPLE  LX.— A  local  bed  plate 34 

D — Volume  Supporters. 

EXAMPLE  X.— A  locomotive  cylinder 34 

EXAMPLE  XI.  —A  jet-condenser 36 

EXAMPLE  XIL— A  surface-condenser 38 

SECTION  II.— GENERAL  SuppoRTERa 

A— Point   Supporters. 

B — Line  Supporters. 

53.  Standards. 

EXAMPLE  XHL—  The  standard  of  a  power  hammer 39 

54.  Comparative  examples. 

C — Surface  Supporters. 

a — Plane   Supporters. 

55.  Fra'mes. 

EXAMPLE  XTV.— Locomotive  frames 45 

b — Developable  Supporters. 

56.  Beds. 

EXAMPLE  XV.— A  prismatic  beam-bed  and  pedestal 48 

D — Volume  Supporters. 

EXAMPLE  XVL— A  tank  bed-plate 49 

EXAMPLE  XVIL — Housing,  or  chambered  frame,  for  a  reversible  rolling 

.     51 


CONTENTS.  V 

PAGE 

EXAMPLE  XVIII.—  Housing  for  a  rolling  mill 54 

EXAMPLE  XTY,  —A  passenger  car  truck.     Practical  remarks 56 


CLASS  II — RECEIVERS. 

A — Point  Receivers. 

B — Line  Receivers. 

C— Surface  Receivers. 

a — Plane  Receivers. 

EXAMPLE  XX. — Locomotive  piston  ;  with  Roth's  steam  piston  packing. .     63 
EXAMPLE  XXI.— Thirty-six,  and  fifty-four  inch  pistons 67- 

b — Developable  Receivers. 
EXAMPLE  XXII.— A  Fourneyron  wheel  plan 68 

c — Warped  Receivers. 

EXAMPLE  XXIII. —A  Jonval  turbine  wheel  and  bucket 71 

d — Double  Curved  Receivers. 
EXAMPLE  XXIV.— The  Swain  central  discharge  wheel 75 


CLASS  HI — COMMUNICATORS. 

A — Point  Communicators. 
EXAMPLE  XXV.— Collins'  shaft  coupling 79 

B — Line  Communicators. 
Band,  Cord,  and  Chain  Wheels. 

THEOREM  I. — A  rotary  motion  of  two  parallel  axes  may  be  maintained 
indefinitely,  and  in  one  and  the  same  direction  for  both,  by  a  band 
passing  directly  around  cylindrical  pulleys  in  the  same  plane,  on 
those  axes  ;  but,  if  the  band  be  crossed,  the  rotations  will  be  in 
opposite  directions ;  but,  in  both  cases,  the  ratio  of  the  velocities 

will  be  constant 81 

THEOREM  II.  — A  band  should  be  crossed  by  giving  it  a  half  twist,  in  a 
plane  perpendicular  to  that  of  the  wheels  which  hold  it :  it  should 
be  shifted,  laterally,  by  operating  on  its  advancing  side,  and  if  ap- 
plied to  a  cone-wheel,  will  work  itself  towards  the  larger  end  of 

the  cone 82 

PROBLEM  I. — To  connect  wheels  lying  in  different  planes,  by  a  band ; 
when  the  intersection  of  their  planes  is  also  a  common  tan- 
gent to  the  two  wheels 84 

PROBLEM  II.— To  connect  band  wheels,  in  different  planes,  when  the 
intersection  of  those  planSs  is  not  a  common  tangent  to  the 
wheels...  86 


Vlli  CONTENTS. 

PAGH 

PROBLEM  VIII.  — To  find  the  radii  of  the  tooth  curves 147 

PROBLEM  IX. — To  find  centres  for  approximate  involute  teeth 148 

EXAMPLE  XXXIV.—  To  construct  teeth  having  separate  faces  and  flanks, 

by  the  odontograph 149 

EXAMPLE  XXXV. — To  construct  approximate  involute  teeth  by  the  odon- 
tograph   152 

EXAMPLE  XXXVI.— Projections  of  bevel  gearing 153 

c — Warped  Communicators. 

EXAMPLE  XXXVII. — The  complete  projections  of  a  screw  and  nut 154 

EXAMPLE  XXXVIII.— The  abridged  drawing  of  screws 157 

Uniform  System  of  Screws 158 

EXAMPLE  XXXIX.— Endless  screws  and  spiral  gear 160 

EXAMPLE  XL. — Detailed  construction  of  a  tooth  in  spiral  gearing 163 

113.  Manufacture  of  worm  wheels 164 


CLASS  IV.— REGULATORS. 
A — Point  Regulators. 
B — Line  Regulators. 

EXAMPLE  XLL— A  fly  wheel 165 

C — Surface  Regulators. 

Plane  throttle  valves.     Single  poppet  valves.     Cage  valves.     Cylindrical 

throttle  valves.     Ball  valves 167 

D — Volume  Regulators. 

Cocks.  Globe  valves.  Water  gates 167 

EXAMPLE  XLII.— Chambered,  or  D  locomotive  slide  valves;  plain,  and 

anti-friction 169 

EXAMPLE  XLIII.— Tremain's  balanced  piston  valve 171 

EXAMPLE  XLIV.— Balanced  poppet  valves.  Data  from  practice 175 

123.  Examples  of  engine  action 179 

EXAMPLE  XL V.— Richardson's  locomotive  and  lock-up  safety  valve 180 

EXAMPLE  XLVI.— A  double  beat  pump  valve 183 

EXAMPLE  XL VII. —A  Cornish  equilibrium  valve 185 

EXAMPLE  XLVIIL  — Giffard's  injector. 185 


CLASS  V.— MODULATORS. 
A— Point  Modulators. 

Idler  pulleys 190 

B — Line  Modulators. 
Escapements.     Band  shifters.     Clutches.     Etc. 190 


CONTENTS.  IX 

O— Surface  Modulators, 
a — Plane  Modulators. 

PAGE 

Variable  crank 191 

b — Developable  Modulators. 

Speed  pulleys 193 

THEOREM  XXI. — If  the  band  be  crossed,  it  will   be    equally  tight   on 

every  pair  of  opposite  pulleys 192 

PROBLEM  X. — To  form  a  set  of  speed  pulleys,  to  give  a  series  of  velo- 
city ratios  in  geometrical  progression 193 

Cone  pulleys.     Dead  Pulleys.     Sectoral  motions.     Elliptic  gears 195 

c — Warped  Modulators. 

The  helicoidal  clutch 197 

d — Double-curved  Modulators. 
Double-curved  speed  pulleys 198 


CLASS  VI.— OPERATORS. 
A— Point  Operators. 

EXAMPLE  XLIX.—  Movable  saw  teeth 199 

EXAMPLE  L.—  Lyall's  positive  motion  shuttle 203 

B — Line  Operators. 
Cutters  (143) 209 

O — Surface  Operators, 
a — Plane  Operators, 

EXAMPLE  LI.— Air  pump  bucket  of  a  marine  engine 209 

b — Developable  Operators, 
c — Warped  Operators. 
THE  SCREW  PROPELLER. 

Preliminary  remarks 210 

Introductory  geometrical  principles 211 

The  helix  and  helicoid 212 

Slip 217 

Lateral  slip 217 

Negative  slip 218 

Irregular  screws , 220 

PROBLEM  XI.— To  construct  a  helix  of  uniform  pitch  and  radius 221 

PROBLEM  XII. — To  construct  the  projections  of  the  common  right 
helicoid,  generated  by  the  radius  of  a  vertical  cylinder 223 


X  CONTENTS. 

PAGE 

PROBLEM  XIII. — To  construct  the  projections  of  a  common  right 
helicoid,  which  is  generated  by  the  diameter  of  a  vertical  cyl- 
inder.   223 

PROBLEM  XIV. — Having  given  either  projection  of  any  element  of  a 

helicoid,  to  find  its  other  projection 224 

PROBLEM  XV. — To  represent  a  common  right  helicoid  by  its  helical 

lines 224 

PROBLEM  XVI.  — To  construct  the  lines  of  a  helicoid,  made  by  its  in- 
tersection with  any  plane  parallel  to  its  axis 225 

PROBLEM  XVII. — Having  given  either  projection  of  any  point  upon  a 

helicoid,  to  find  its  other  projection 226 

PROBLEM  XVIII. — To  develope  one  or  more  given  helices 226 

PROBLEM  XIX. — From  the  circular  projection  and  development  of  a 

helix,  to  construct  its  spiral  projection 227 

PROBLEM  XX. — To  construct  a  helicoid  of  axial  expanding  pitch,  by 

means  of  its  helical  lines 228 

PROBLEM  XXL — To  develope  the  four  helices  last  drawn 228 

PROBLEM  XXII. — To  make  the  projections  of  a  helicoid  of  radially 

expanding  pitch 229 

PROBLEM  XXIII.  —To  develope  the  helices  shown  in  the  last  problem .   230 
PROBLEM  XXIV. — To  construct  the  projections  of  the  acting  faces  of 

a  four-bladed  common  screw  propeller 231 

EXAMPLE  LIL— To  represent  variously  limited  propeller  blades,  with 

their  concentric  and  radial  sections 232 

Ideas  expressed  in  modified  forms  of  Screws 235 

Historical  note 236 

EXAMPLE  LHL—  The  screw  of  the  "  Dunderberg." 238 

D — Volume  Operators. 
EXAMPLE  LIV.— Andrews'  centrifugal  pump 240 


BOOK  II. 

COMPOUND  ELEMENTS,  OR  SUB-MACHINES. 
SUPPORTERS. 

EXAMPLE  LV.— A  compound  chuck 245 

COMMUNICATORS. 

EXAMPLE  LVI. — A  beam-engine  main  movement 249 

EXAMPLE  LVII.—  Wheeler's  tumbling-beam  engine 250 

EXAMPLE  LVIII.— An  eight  day  clock  train 252 

Other  trains 252' 

Change  wheels 256 

THE  SLIDE  VALVE  AND  ITS  CONNECTIONS. 

General  description  of  parts 257 

General  action  .  . 259 

Modifications  and  adjustments 260 


CONTENTS.  XI 

PAGE 

Definitions ' 261 

THEOREM  XXII. — In  either  mode   of   connection  the  velocity  of  the 

crank  pin  is  uniform,  and  that  of  the  piston  is  variable 268 

THEOREM  XXIII.  — The  piston  positions,  corresponding  to  crank  pin  po- 
sitions, which  are  equidistant  from  the  same  dead-point  are  iden- 
tical, for  each  connection  separately. .  r 264 

THEOREM  XXIV. — The  segments  of  the  double  stroke  are  equal,  in  the 
direct  connection,  and  the  front  one  is  the  greater  in  the  indirect 

connection.     Conversely,  etc 264 

Natnml  zero  paints  of  the  piston  and  crank-pin  motions,  and  segments  of 

the  double  stroke 265 

THEOREM  XXV. — The  crank  piston  is  ahead  of  the  yoke  piston  during 
the  stroke  toward  the  shaft,  and  behind  it  during  the  opposite 

stroke 266 

Cut- O/ 267 

THEOREM  XXVI  — The  effect  of  a  given  angular  advance  of  the  eccen- 
tric will  be  to  afford  "admission"  for  a  new  stroke,  "cut-off," 
"  exhaust  closure,"  and  release,  all  at  an  equal  number  of  degrees 

before  reaching  a  dead-point 267 

THEOREM  XXVII. — The  effect  of  a  given  lap,  alone,  corresponding  to 
an  equal  number  of  degrees  from  the  zero  diameter,  is,  to  post- 
pone admission  for  an  equal  number  of  degrees  beyond  the  dead- 
point  ;  to  produce  cut-off  at  the  same  number  of  degrees  beyond 
the  dead-point ;  with  release  and  exhaust  closure  at  the  dead-point.  268 
PROBLEM  XXV.  — To  produce  a  cut-off  at  a  given  crank-pin  position, 

without  preventing  proper  admission,  etc 269 

PROBLEM  XXVI. — To  determine  the  exhaust  closure  and  release,  for 

the  adjusted  cut-off  and  admission 270 

THEOREM  XXVIII.  — The  travel  of  a  valve,  with  lap,  is  the  sum  of  twice 

the  lap,  added  to  twice  the  steam  port  opening 270 

THEOREM  XXIX. — Inside  lap  prolongs  expansion,  and  hastens  compres- 
sion ;  while  inside  clearance  hastens  the  release,  and  postpones  the 

beginning  of  compression 271 

PROBLEM  XXVII. — To  determine  the  effect  of  the  eccentric  upon  the 

valve  motion  and  to  counteract  it  in  part 272 

Distribution  of  power. 273 

Lead 273 

PROBLEM  XXVIII. — To  provide  a  certain  lead  angle,  without  disturb- 
ance of  the  cut-off 274 

PROBLEM  XXIX.— To  determine  the  effect  of  lead  on  exhaust  closure, 

release  and  travel 274 

THEOREM  XXX.— The  angular  advance,  estimated  from  the  zero  radius 
hitherto  taken,  is  equal  to  the  sum  of  the  lap  and  lead  angles, 

estimated  from  the  same  point 275 

THEOREM  XXXI. — When  the  steam  port  is  open  by  the  amount  of  the 
lead,  the  exhaust  opposite  port  is  open  for  exhaust  by  the  amount 

of  the  lap  and  lead 275 

Port  opening 276 

Summary  of  elements 278 


Xii  CONTENTS. 

PAGB 

PKOBLEM  XXX. — To  reverse  the  motion  of  an  engine.     Drop  hook. . .  280 

EXAMPLE  LIX.— A.  Stephenson  link  motion 283 

To  find  one  position  of  the  link 285 

Data  for  finding  any  position  of  the  link 2':'  i 

To  adjust  the  model 287 

Remarks  and  results * 2Q8 

EXAMPLE  LX.— Data  of  valve  motions 290 

I.— Of  a  15"  x  22"  cylinder 290 

II.— Of  a  16"  x  24"  cylinder 291 

III.— Of  an  18"  x  22"  cylinder 291 

Experimental  determinations. 293 

Setting  the  valve  motion  of  a  locomotive. 294 


REGULATORS. 

Governors. 

Elementary  Principles 297 

EXAMPLE  LXL—  Chubbuck's  fan  throttle  governor 300 

EXAMPLE  LXIL— The  Huntoon  oil  throttle  governor 302 

EXAMPLE  LXIIL— Wright's  variable  cut-off  by  the  governor 304 

EXAMPLE  LXIV.— Babcock  and  Wilcox  governor  and  variable  cut-off. . .  307 

Indicator  diagrams 314 

EXAMPLE  LXV.— The  Putnam  Machine  Co.'s  variable  cut-off 320 

EXAMPLE  LXVI.—  The  Rider  cut-off 321 

EXAMPLE  LXVII.— Sibley  and  Walsh's  water-wheel  governor 322 


MODULATORS. 

EXAMPLE  LXVIII.— Compound  speed  and  feed  motions 325 

EXAMPLE  LXIX.— Whitworth's  quick-return  motion 327 

EXAMPLE  LXX.— Mason's  friction  pulleys  and  couplings,  or  clutches 328 

EXAMPLE  LXXI. — Reversing  gear  for  the  compound   Rolling-Mill  En- 
gine    332 

EXAMPLE  LXXIL— Bond's  escapement,  No.  2 334 

EXAMPLE  LXXHL—  Bond's  auxiliary  pendulum  gravity  escapement 337 


PREFACE. 


THIS  book  may  be  compared  to  an  excursion  train.  Everything 
mechanical  has  called,  or  striven  for  a  place  in  it,  if  only  to  cling  to 
the  platform  of  briefest  mention.  Yet  not  a  tithe  even  of  the  beau- 
ties of  mechanism  have  been  admitted,  for  want  of  room.  Indeed, 
one  of  the  most  arduous  labors  connected  with  the  composition  of 
this  work  has  been  to  keep  out  the  nearly  irrepressible  crowd  of 
topics  and  examples  that  were  pressing  into  it.  Those  that  have 
been  admitted  have  been  selected  with  great  care,  after  personal  in- 
spection in  machine  shops,  and  from  valuable  circulars,  correspon- 
dence, and  published  authorities. 

Other  examples  have  been  partially  represented  by  woodcuts  and 
brief  notices,  or  have  necessarily  been  excluded,  and  remanded  back 
to  the  great  world  of  mechanism. 

In  either  case  the  governing  idea  has  been,  to  develope  the  compre- 
hensive scheme  of  the  General  Table  proportionately,  though  briefly, 
with  examples  that  should  be  American  (mostly),  new,  and  good. 

There  are  at  least  six  topics  in  this  work,  about  which  the  trouble- 
some problem  has  been  to  touch  them  at  all,  unless  superficially, 
without  devoting  a  volume  to  each.  These  are,  Turbines,  Gearing, 
Propellers,  Valve  motions  •  Governors,  with  or  without  Variable  Cut- 
offs ;  and  Trains  of  gearing,  as  clock  trains. 

Of  turbines,  I  have  only  taken  one  of  each  of  the  three  essentially 
different  kinds,  with  a  simple  description  of  its  construction  and 
action. 

On  gearing,  I  have  been  reasonably  full,  giving  the  substance  of 
what  need  be  known  in  behalf  of  proper  practice,  and  with  simple 
explanations. 

As  to  propellers,  their  theory  is  so  intricate,  owing  to  the  variety 
and  indefiniteness  of  the  data  for  calculations  concerning  them ;  and 


XIV  PREFACE. 

numberless  experimental  results  are  so  full  and  accessible  in  Bourne 
and  in  similar  works,  that  I  have  mostly  interested  myself  in  giving 
exact  instruction,  nowhere  else  accessible  so  far  as  I  know,  about 
making  their  projections  ;  so  as  indirectly  to  correct  grievous  errors, 
and  supply  deficiencies,  which  have  been  found  in  print  on  this 
subject. 

With  the  ample  geometrical  treatment  of  valve  motions  by  Mr. 
Auchincloss,*  and  the  masterly  analytical  work  of  Prof.  Zeuner,  to 
supplement  the  little  that  I  have  found  room  for  on  the  same  topic, 
I  have  had  a  narrowly  limited  and  definite  object  in  view  in  what  I 
have  had  to  say  on  that  subject.  The  treatment  of  valve  motions  in 
the  encyclopaedias  and  the  extended  serial  works,  like  Colburn's 
Locomotive  Engineering,  is  generally  unavailable.  The  works  of 
Auchincloss  and  Zeuner,  presuppose,  expressly  or  impliedly,  a  good 
deal  of  familiarity  with  the  subject.  But  many  persons  are  wholly 
unfamiliar  with  it,  and,  unless  apt  to  conceive  readily  of  combined 
motions,  find  it  a  puzzling  subject.  My  work  has  therefore  been 
little  more  than  to  begin  at  the  very  beginning,  and  virtually  to  pre- 
pare for  the  beginner  an  introduction  to  those  works.  More,  indeed, 
could  not  be  attempted  in  a  volume  in  which  so  many  other  topics 
have  been  introduced. 

Governors,  a  plaything  of  American  ingenuity,  have  been  sum- 
marily, but  with  the  most  instructive  variety  attainable  within  small 
limits,  passed  over  with  the  selection  of  the  most  marked  varieties 
of  governor  and  valve. 

Trains  of  gearing,  though  very  briefly  noticed,  have,  it  is  hoped, 
been  so  treated  as  to  afford  some  clear  and  accurate  ideas  on  that 
subject,  as  a  foundation  for  further  study. 

The  classified  table  of  machines  has  been  prepared  with  great  care, 
and  compared  with  that  in  the  Encyclopaedia  Britannica  by  Prof. 
Ptankine,  which  is  quite  different,  without  material  alteration  in  the 
result.  I  have  endeavored,  in  the  paragraphs  immediately  preceding 
the  table,  so  to  distinguish  machines  from  instruments,  as  to  ration- 
ally exclude  engineering,  astronomical  and  musical  instruments  from 
the  province  of  machines,  in  which  he  includes  them;  contrary  to 
those  common  usages  of  speech,  which  I  believe  will  be  found  upon 
analysis  to  be  grounded  on  real  differences. 

*  Graduate  of  the  R.  P.  L,  1862. 


PREFACE.  XV 

Still,  the  number  and  uses  of  machines  are  so  endless,  that  I  can- 
not profess  to  have  found  a  strictly  scientific,  and  therefore  exhaustive 
classification  of  them. 

A  word  now  as  to  the  intended  use  of  this  book  in  the  class-room 
may  be  considered  seasonable.  Previous  to  its  appearance,  the  sub- 
ject of  it  was  taught  orally,  and  with  no  small  labor,  to  classes, 
which,  in  their  turn,  cquld  progress  neither  so  rapidly  nor  pleasantly 
as  if  provided  with  a  text-book.  The  present  volume  is  naturally 
much  fuller  than  an  oral  course  could  well  be,  and  is  intended  as  a 
text-book  upon  which  daily  interrogations  and  black-board  exercises 
are  to  be  held,  as  well  as  a  manual,  to  be  constantly  open  before  the 
student  for  a  guide  in  the  preparation  of  his  drawings. 

With  the  plates  of  uniform  size  for  each  student,  so  that  they  can 
be  agreeably  bound  together,  but  with  a  choice  as  to  that  size,  from 
quarter  super-royal  to  semi-super-royal,  until  the  best  size  can  be  ex- 
perimentally determined,  it  may  be  well,  wherever  practicable,  to 
require  that  one  of  them  should  be  constructed  from  actual  measure- 
ments, made  by  the  student,  and  accompanied  by  a  plate  containing 
an  inked  copy  of  the  sketches  and  measurements. 

Some  of  the  plates  should  have  the  measurements  recorded  sub- 
stantially in  the  style  of  office  practice,  and  they  should  generally  be 
titled,  in  addition  to  the  general  title-page  of  the  collection.  Or  there 
should  be  a,  separate  plate  containing  the  several  titles. 

The  "  heavy  lines  "  are  omitted,  or  displaced  in  some  plates,  as  an 
exercise  for  the  student  in  supplying  or  correcting  them. 

Finally,  the  following  lists  will  show  to  what  helping  friends  I  am 
indebted,  and  what  sources  of  information  I  have  diligently  consulted. 
Also  the  signatures  of  student  draftsmen,  of  the  classes  of  '70  and  '71, 
R.  P.  I.,  on  many  of  the  plates  will  always  happily  remind  me  how 
kindly  my  labors  in  that  direction  were  lightened. 

TROY:  November,  1870. 


XVI 


ESTABLISHMENTS    VISITED    OR    DRAWN    UPON    FOR    MATERIALS    USED    IN 
THIS    WORK. 

American  Saw  Co  ..........................  Trenton,  N.  J. 

Andrews  Bros  ..............................  New  York. 

Atlantic  Works  ...........................  .  Boston. 

Babcock  and  Wilcox  Eng.  Works  ..............  New  York. 

Bement  and  Dougherty  ......................  Philadelphia. 

Bessemer  Steel  Works  .......................  Troy,  N.  Y. 

Boston  and  Albany  R.  R.  Shops  ..............  Boston. 

Boston,  Hartford  and  Erie  R.  R  ..............  " 

Bond's  Chronometer  Rooms  ..................  " 

Brooklyn  Water  Works  .....................  Brooklyn. 

Brown's  Machine  Works  ....................  Troy,  N.  Y. 

Bullard  and  Parsons  .........................  Hartford,  Conn. 

Cambridge  Machine  Works  ..................  Cambridge,  N.  Y. 

Chubbuck  &  Sons  ..........................  Boston. 

Collins'  Turbine  Works  ......................  Norwich,  Conn. 

Delamater  Iron  Works  ......................  New  York. 

Gurley  W.  &  L.  E  ..........................  Troy,  N.  Y. 

Harmony  Mill  .............................  Cohoes,  N.  Y. 

Hopedale  Mach.  and  Furnace  Co  ..............  Hopedale,  Mass. 

Hinckley  &  Williams'  Loc.  Works  ............  Boston. 

Horton  E.  Machine  Works  ...................  Hartford,  Conn. 

Hotchkiss,  Power  Hammers  ..................  New  York. 

Huntoon  Governor  Co  .......................  Boston. 

Jones  and  Laughlin  .........................         Pittsburgh,  Pa. 

Judson  Governor  Works  .......  .  .............  Rochester,  N.  Y. 

Lowell  Machine  Shop  .......................  Lowell,  Mass. 

Ludlow  Yalve  Co  ...........................  Troy,  N.  Y. 

Lyall  Positive  Motion  Loom  Co  ...............  New  York. 

Mason  Y.  W.  Friction  Clutches,  etc  ............  Providence,  R.  I. 

McMurtrie  <fc  Co.,  Machine  Agency  ...........  Boston. 

Milwaukee  &  St.  Paul  R.  R.,  E.  M.  Hall,  Supt. 

Power  ................................  Milwaukee,  Wis. 

Morgan  Iron  Works  ........................  New  York 


PREFACE.  Xvii 

New  York  Central  R.  R.  Shops Albany,  N.  Y. 

Novelty  Iron  Works New  York. 

Pennsylvania  R.  R.  Car  Shops Altoona,  Pa. 

Putnam  Machine  Works Fitchburg,  Mass. 

Rensselaer  Iron  Works Troy,  N.  Y. 

Ruggles'  Machine  Works Poultney,  Vt. 

Sault  M.  &  T.  Co New  Haven,  Conn. 

Sellers,  Wm.  &  Co Philadelphia. 

Shaw  &  Justice,  Hammers 

Sfcarbuck  Bros.,  Engineers Troy,  N.  Y. 

Steere,  E.  N.,  Cotton  Machinery Providence,  R.  I. 

Swain  Turbine  Co Chelmsford,  Mass. 

Tremain,  Balance  Valves , Chicago,  111. 

Troy  &  Boston  R.  R.  Machine  Shop Troy,  N.  Y. 

U.  S.  Navy  Dep't Washington,  D.  C. 

Washington  Iron  Works Newburgh,  N.  Y. 

Wheeler,  N.  W.,  Eng.  Office New  York. 


PERIODICALS    AND    WORKS    OF    REFERENCE    CONSULTED. 

American  Artisan. 

Auchincloss,  T.ink  and  Valve  Motions. 

Belanger,  Cinematique. 

Borgnis,  Composition  of  Machines,  1818. 

Bourne  on  the  Screw  Propeller. 

"       Catechism  of  the  Steam  Engine. 
Brown,  H.  T.,  507  Mech'l  Movements. 
Burn,  R.  S.,  Mech.  and  Mechanism. 
Colburn,  Locomotive  Engineering. 
Engineer,  The. 
Engineering. 

Engineer  and  Mach.  Drawing  Book. 
Fairbairn,  Mach.  of  Transmission. 
Francis,  Hydraulic  Experiments. 
Hughes  on  Water  Works,  Weale's  Series. 


PREFACE. 

Imperial  Cyclopaedia  of  Machinery. 

Jour,  of  Franklin  Inst.,  1860,  1864,  1867-70. 

Joynson,  Gearing. 

King,  W.  EL,  Notes  on  Steam. 

Leroy,  Geometric  Descriptive,  Applications. 

Long  &  Buel,  Cadet  Engineer. 

Olivier,  Geometric  Descriptive,  Applications. 

R.  P.  I.  Collections  of  Mechanical  Lithographs. 

Roebling,  Wire  Rope  Transmission. 

Scientific  American. 

Sellers  on  a  System  of  Screw  Threads. 

Weisbach,  Mechanics. 

Weissenborn,  Amer.  Eng'g  illustrated. 

Willis'  Principles  of  Mechanism. 

Zeuner,  on  Valve  Gears. 


GENERA 


FUNCTIONAL    CLASSII 

ELEMENTS  OF 

FIXED  ELEMENTS.    SUPPORTERS. 

MACHINES. 

LocaL 

General. 

RECEIVERS. 

COMMUNICAT< 

Pillow  Blocks.* 

Chain  hooks. 

Crank  Pins. 

POINT 

Axle  Box.        * 

Block  Cross  Hea 

ELEMENTS. 

Hangers.           * 

Fixed  Couplings 

Footsteps.        * 

Winches. 

(  Bands 

Guides.     Straight.* 

Drill  posts. 

Treadles. 

Flexible  J.  Cords 

Curved. 

Standards.* 

Engine  hand  levers. 

(Cham 

LINE 

Arms. 

Solid    beam-frames    or 

Levers  of  Horse  powers. 

f  Cranks 

ELEMENTS. 

beds.* 

Rocker 

Connec 

rods. 

Rigid.       Links. 

Excent 

rods. 

Workir 

I     bearr 

CATION. 

PLANE. 

Planer  tables. 
Face  plates. 
Flat  brackets. 

Plane  bed  plates. 
Flat  Frames.  (  Web.* 

Flat  pistons.     * 
Endless     platforms     in 
Horse  powers. 

Excentrics.    * 

h 

1    beam.* 

1 

X 

I 

Cylindrical  brackets. 
Local  prismatic  beds.* 
Staffing  boxes.            * 

Prismatic  beds.* 
Corliss      Vert.      Eng. 
Frames. 

Cylindrical  water  wheel 
floats. 
Fourneyron         Turbine 

Band  wheels.  * 
Spur  wheels.  * 
Bevil  wheels.  * 

3 

x 

Buckets.* 

1 

a 

ft 

1 

a 

. 

JonvalTurbine  buckets.* 

Hyperboloidal  w 

§ 

H 

I 

Turbine  guides.  Jonval. 

Wind  mill  vanes. 

Screws.* 

fe 

« 

Worm  wheels.* 

1 

* 

Spiral  gear.* 

| 
g 

Bell-shaped  pedestals. 

Segmental  spherical  pis- 
tons.* 

Swain     turbine     buck- 

ets.* 

I 

Slide  rests. 

VOLUME 

Valve  Chests.          * 
Steam  Cylinders.    * 

Bed  Plates—  Tank.    * 

Overshot    water    wheel 
buckets. 

ELEMENTS. 

"      Condensers.* 

Chambered  Frames.* 

Pump  Barrels. 

Etc. 

Housings.                   * 

Trucks.                       * 

*  Illustrated  in  the  plates     j 


TABLE. 


ON. 

COMPOUND  ELEMENTS  OR  SUB- 
MACHINES. 

MOVING  ELEMENTS. 

REGULATORS. 

MODULATORS. 

OPERATORS. 

SUPPORTERS. 

Governor  halls.* 

Idler  pulley. 
Escape  wheel. 

Saw  teeth. 
Shuttles. 

Compound  Chucks. 
"          Slide  Rests. 
"          Tool  Holders. 

Fly  wheels.        * 

Band  shifter  arms. 
Pin  clutches. 
Simple  slide  rests. 

Drills. 
Cutters,  Helical  as  in 
Hay  cutters  and 
Ruggles'    Slate    trim- 
mers. 

COMMUNICATORS. 

Beam  Engine  Connections.  * 
Tumbling  Beam  Movements.* 
Clock  Trains.* 

REGULATORS. 

Throttle  valves. 
Puppet  valves. 
Plat  slide  valves. 
Plat    oscillating    valves. 
(Corliss.) 

Variable  orank. 

Ah-  pump  buckets.* 
Printing  press  platens. 

Valve  Motions.* 
Governors.  Ball*  "1           f  Throttle 
Valve 
Fan*  }•  for  -j        or 
1     Steam 
Oil  *J           [    Valve. 
Gauges. 

Cage  valves. 
Cylindrical            throttle 
valves. 

Cone  pulleys. 
Speed     " 
Dead       " 
Sectoral  motions. 
Elliptic  gears. 

Bending,     polishing, 
and  shaping  rolls. 

Helicoidal  clutch. 

Screw  propellers.* 

MODULATORS. 

Feed  Motions. 
Band  Shifters. 
Quick  Returns.* 
Friction  Clutches. 
Componnd  reversing  gear.* 
Escapements.* 

Ball  valves. 

Paraboloidal  pulleys. 

Clock  bells. 

Cocks,  and  water  gates. 
Chambered  slide  valves.* 
Balanced  poppet  valves.* 
Lock  up  valve,  safety.     * 
Double        beat       pump 
valves.* 
Giffard's  injector.* 

Steam  Hammers. 
Pile     driving     Ham- 
mers. 
Pump  plungers. 

of  the  others,  by  woodcuts. 


ELEMENTS 

oy 

MACHINE    CONSTRUCTION   AND   DRAWING, 


BOOK  FIRST, 

SIMPLE  OE  SINGLE  ELEMENTS  OF  MACHINES. 

PART  I. 
INTRODUCTION. 

GENERAL   PRINCIPLES. 

1.  Bodies,  in  addressing  the  eye,  exhibit  not  only  the  attri- 
butes of  color,  transparency,  or  opacity ;  polish,  or  roughness ; 
but  the  two  fundamental  geometrical  attributes  of  Form  and 
Size. 

2.  FORM  is  a  determinate  arrangement  of  an  assemblage  of 
points,  according  to  some  law.     It  depends  upon  the  relative 
lengths  and  directions  of  the  bounding  lines  of  a  body. 

3.  SIZE  is  the  amount  of  space  occupied  by  a  body,  and  is 
due  to  the  extent  of  its  bounding  lines,  as  compared  with  a  unit 
of  measure. 

4.  Drawings  may  represent  objects,  in  respect  to  their  size, 
as  larger,  or  smaller  than  they  really  are ;  or,  in  their  real  size; 

5.  Drawings  which  represent  the  apparent  forms  of  bodies 
as  presented  to  the  eye,  are  called  perspective  drawings,  or  pic- 
tures /  and  are  intended  chiefly  for  ornament,  or  for  popular 
illustration. 

6.  Drawings  which  represent  the  real  forms  of  objects,  as  de- 
termined by  the  sense  of  touch,  in  taking  measurements,  are 
called  projections.     Since  such  drawings  show  the  real  proper- 


tions  of  objects,  they  constitute  a  graphic  language,  by  which 
the  thoughts  of  a  designer  can  be  most  clearly  conveyed  to  a 
workman,  who  can  thence  construct  the  objects  represented. 
Hence  projections  are  often  called  working  drawings. 

7.  While  working  drawings  represent  the  real  forms  of  ob- 
jects ;  they  represent  them,  in  a  majority  of  cases,  in  less  than 
their  real  size.  But  to  preserve  the  true  proportions  in  the 
drawing,  all  the  parts  of  the  object  must  be  similarly  reduced 
in  the  drawings.  This  is  what  is  called  drawing  fy  scale.  That 
is,  each  distance,  as  a  foot,  on  the  object,  is  represented  by  some 
less  distance,  as  an  inch,  or  a  quarter  inch,  etc.,  on  the  drawing. 


8.  The  only  scales  necessary  to  be  understood  by  students  of 
the  present  work,  are  the  linear  scale,  and  the  diagonal  scale  of 
equal  parts,  which  we  will  now  explain. 


J2  0  1  2 

FIG.  1. 


Fig.  1  represents  a  plain  linear  scale  of  three  feet  to  the  inch, 
*ach  of  its  units  as  from  0  to  1  being  one-third  of  an  inch. 
The  equal  space  from  0  to  12,  is  divided  into  twelve  equal  parts, 
representing  inches.  Thus,  from  4  to  the  fifth  mark  to  the  left 
of  0,  represents  four  feet  and  five  inches,  and  is  therefore  called 
four  feet  and  five  inches.  For  brevity  this  is  written  4':5". 

9.  Other  linear  scales  of  equal  parts,  being  similarly  con- 
structed, can  readily  be  understood  from  this  example.  The 
ivory  scales  used  by  draftsmen,  contain  a  variety  of  such  single 
scales,  with  the  left  hand  unit  divided  both  into  tenths  and 
twelfths.  It  also  contains  others,  expressed  in  inches  to  the  foot, 
as  one  inch  to  one  foot,  three-fourths  of  an  inch  to  a  foot,  etc.. 
and  numbered  accordingly  IN  =  inch ;  £• ;  f ;  £ ;  etc. 


5             dO                  1                 2                 3                 4                 5 

/  /  /  /  /! 

/  4  I  1  j\ 

I              1 

1*1     ' 

1 

'  /  /  /  /  1 

i 

10.  Fig.  2  represents  a  simple  diagonal  scale  of  units,  5ths ; 


MACHINE   CONSTRUCTION   AND   DRAWING.  3 

and  4ths  of  the  5ths.  The  space  0  —  5',  which  is  equal  to  0  —  1, 
etc.,  is  then  divided  into  five  equal  parts  ;  and  so  is  ac.  The 
five  equidistant  horizontal  lines  afford  four  equal  spaces.  We 
then  reason  thus  :  If  in  coming  down  four  spaces  on  Ob,  to  b, 
we  depart  from  the  vertical  Oa  by  the  space  ab,  which  is  one- 
fifth  of  the  unit  01,  in  coming  down  one  space,  we  should  de- 
part one-fourth  of  ab,  which  equals  one-twentieth  of  01.  We 
thus  have  the  rule  for  reading  the  scale  :  proceed  to  the  left  of 
0  as  many  spaces  as  there  are  5ths  required,  and  then  down  on 
the  diagonal  thus  reached  as  many  spaces  as  there  are  4ths  of 
5ths  required.  Thus  the  distance  between  the  stars  is  3  units, 
3-fifths  and  2-fourths  of  a  fifth,  or 


All  other  diagonal  scales,  including  the  more  familiar  deci- 
mal diagonal  scale,  are  made  and  used  in  a  similar  way  ;  so  that 
if  any  one  of  them  be  rationally  and  fully  comprehended,  all 
others  may  easily  be  understood. 

If,  as  is  sometimes  done,  the  diagonals  were  drawn  in  the  di- 
rection ad,  the  numbers  0,  1,  2,  etc.,  would  be  on  the  lower 
line  ac. 

11.  In  regard  to  the  manual  operations  of  machine  drawing, 
the  proper  standard  of  precision  should  be  carefully  observed. 
That  is,  the  student  should  always  imagine  himself  in  a  drafting 
office,  working  as  if  his  compensation,  or  position,  depended 
upon  the  accuracy  of  his  work.     And  the  latter  should  be  the 
same  as  if  his  plates  were  to  form  working  drawings  for  the 
actual  construction  of  finished  machinery.     To  this  end,  all 
points  should  be  accurately  located,  and  finely  marked  /  and 
all  lines  should  be  finely  drawn  with  none  but  the  hardest  pen- 
cils, and  exactly  through  \he  proper  points. 

In  much  of  machine  drawing,  the  distances  to  be  laid  off  are 
numerous,  and  quite  small,  hence  the  fine  spacing  dividers,  pens, 
and  pencils,  are  of  especial  use,  as  well  as  the  most  accurate 
scales. 

12.  The  instruments  called  scales,  are  simply  pieces  of  metal, 
ivory,  wood,  or  paper  containing  a  variety  of  linear  and  other 
scales. 

The  leading  forms  of  scales  are  edge  scales  and  surface 
scales.  An  edge  scale  is  a  scale  whose  graduations  are  on 
the  edge  of  the  substance  containing  it.  This  form  of  scale  is 


4  ELEMENTS   OF 

most  convenient,  because  a  distance  can  be  transferred  from  it 
to  the  paper,  directly,  by  laying  the  scale  on  the  paper  and 
pricking  off,  with  a  needle-point,  the  extremities  of  the  given 
distance.  The  best  form  of  edge  scale  is  the  triangular  scale, 
which  contains  six  linear  edge  scales.  The  other  form,  or  flat- 
edge  scale,  having  its  edges  chamfered  on  one  side  to  ensure 
greater  accuracy  in  its  use,  can  conveniently  carry  but  two 
edge  scales,  except  as  two  or  more,  each  of  which  is  just  double 
the  other,  may  lie  against  the  same  edge. 

13.  Surface  scales  are  flat  pieces  of  some  hard  material, 
usually  ivory,  containing  a  set  of  various  linear  scales,  side 
by  side,  and,  all  together,  covering  the  surface  of  the  instrument. 
These  give  more  scales  on  a  single  instrument  than  edge 
scales;  but  to  transfer  a  distance  from  them  to  paper,  we 
must  proceed  indirectly  by  taking  up  this  distance  in  a  pair 
of  dividers,  and  then  laying  it  down  on  the  paper. 


Elements  of  Projections. 

14.  The  following  brief  rehearsal  of  the  elements  of  pro- 
jections may  assist  many,  or  all  who  make  use  of  this  A'olume. 

A.  solid  has  three  dimensions,  at  right  angles  to  each  other. 

Therefore  if  a  horizontal 
plane,  as  EQ,  Fig.  3,  be 
placed  parallel  to  two  of 
the  dimensions,  as  AB  and 
BC,  of  a  solid,  and  if  the 
latter  be  then  viewed  in  a 
direction,  Aa,  perpendicu- 
lar ,to  the  plane  RQ,  those 
dimensions  can  be  seen,  cor- 
rectly represented,  in  length 
and  direction,  upon  that 
plane,  as  at  db  and  be. 

The  figure  abed  is  thus 
equal  to  the  visible  top  of 

the  given  body,  and  is  called  its  horizontal  projection  ;  or,  in 

the  language  of  practice,  its  plan. 

15.  In  like   manner,   if   a    vertical   plane,    US,    be    taken 
parallel  to  the  dimensions,  AB  and  AG,  and  if  it  be  viewed 


MACHINE   CONSTRUCTION   AND   DRAWING.  5 

perpendicularly,  as  in  the  direction  Del',  these  dimensions  can 
be  correctly  shown  on  that  plane.  The  figure  d'c'e'f,  equal  tc 
DCEF,  is  called  the  vertical  projection,  or  the  elevation  of  the 
given  body. 

Thus  we  see  that  the  two  projections  of  a  body,  taken 
together,  show  its  three  dimensions,  when  the  latter  are  parallel 
to  the  planes  KQ  and  RS,  which  are  called  the  planes  of 
projection. 

16.  Observe  now  that  d'g,  the  height  of  the  vertical  pro- 
jection of  D  above  the  ground  line,  is  equal  to  Dd,  the  height  of 
D,  itself,  above  the  horizontal  plane.     In  like  manner,  en,  the 
distance   of  the  horizontal  projection   of  C  from  the  ground 
line,  is  equal  to  the  perpendicular  distance  of  C,  itself,  from  the 
vertical  plane. 

That  is :  The  perpendicular  distance  of  a  point  in  space 
from  either  plane  of  projection,  is  equal  to  the  distance  from, 
the  ground  line  to  its  projection  on  the  other  plane. 

17.  Analyzing  the  figure  a  little,  we  see  that  when  a  line,  as 
AB,  is  parallel  to  a  plane  of  projection,  its  projection  ab,  or 
c'd',  upon  such  plane,  is  equal  and  parallel  to  itself.     Also  if  a 
line,  as  DF,  perpendicular  to  the  horizontal   plane,  or  DA, 
perpendicular  to  the  vertical  plane,  is  perpendicular  to  a  plane, 
its  projection  on  that  plane,  as  d  ord'  respectively,  is  a  point; 
and  on  the  other  plane,   as  at   d'f  and  da,  respectively,  is 
perpendicular  to  the  ground  line,    and  parallel  to  the  line 
in  space.     With  this  suggestion,  the  reader  can  make  out  the 
projections  of  lines  in  other  positions,  as  the  diagonals,  AC,  DE, 
AF  and  AE,  not  shown. 

18.  Summary  of  definitions. 

A  plane  of  projection  is  one  on  which  an  object  is 
represented. 

A  projecting  line  is  a  line  from  any  point  of  an  object, 
perpendicular  to  a  plane  of  projection;  and  it  represents  the 
direction  in  which  the  object  is  looked  at. 

The  projection  of  any  point,  is  the  intersection  of  the 
projecting  line  of  that  point  with  a  plane  of  projection. 

The  projection  of  any  object  is  the  figure  formed  by  joining 
the  projections  of  the  bounding  points  of  that  object. 

The  intersection,  R/i,  of  the  two  planes,  is  called  the  ground 
line.  So  simple  an  apparatus  as  a  folding  slate  or  sheet  of  stiff 


ELEMENTS   OF 


paper,  with  the  leaves  placed  horizontally  and  vertically,  and  a 
few  straws,  will  serve  to  illustrate  the  principles  here  stated. 

19.  The  planes  of  projection,  which  are  at  right  angles  to 
each  other  in  space,  coincide  upon  paper.     This  is  accomplished 
hy  supposing  the  vertical  plane,  RS,  Fig.  3,  to  revolve  backward 

about  the  ground  line,  until  it  co- 
incides with  the  horizontal  plane 
produced  backwards. 

Supposing  now  the  planes  to 
be  of  indefinite  extent,  Fig.  3 
would  be  thus  transformed  into 
Fig.  4,  which  shows  the  pro- 
jections abed  and  d'c'e'f,  as 
they  really  are,  instead  of  pictori- 
ally,  as  in  Fig.  3.  GL,  the  ground 
line,  represents  ~Rn  in  Fig.  3. 

The  two  projections,  as  d  and 
d',  of  tJie  same  point,  are  thus 
in  the  same  perpendicular  to 
the  ground  lm.e.  This  should  be  carefully  remembered. 

20.  A  point  is  named  hy  naming  its  projections.     Thus 
the  point  ddf,  Fig.  4,  means  the  point  itself,  D,  Fig.  3,  whose 

f  projections  are  d  and  d.     The 

like  is  true  of  lines.  Thus  the 
line  do — d'o',  Fig.  4,  means  the 
line  DC,  Fig.  3,  whose  projec- 
tions are  dc  and  d'c '. 

21.  Resuming,  now,  the  con- 
clusion of  (15)  if  the  dimensions 
of  a  body  are  not  parallel  to  the 
planes  of  projection,  they  may  be 
made  so  either  by  turning  the 
body,  or  by  taking  a  new  plane 
of  projection.  In  turning  a  body, 
it  is  sufficient  to  study  the  motion 
of  one  of  its  points. 

This  understood,  the   follow- 
ing principles  pertain  to  the  revo- 
lutions of  points 
a — If  a  point  as  mm',  Fig.  5,  revolve  about  a  vertical  axis, 


MACHINE   CONSTRUCTION  AND   DRAWING.  7 

as  A — A'B'  (see  DF,  Fig.  3),  it  will  describe  a  horizontal  arc, 
as  mm" — m'm"' ',  whose  horizontal  projection,  mm" ,  will  be 
an  equal  arc,  with  centre  at  A,  and  whose  vertical  projection, 
m'm"' ,  will  be  a  straight  line  parallel  to  the  ground  line. 

b — Similarly,  if  a  point  mm',  Fig.  6,  revolve  about  an  axis, 
AB — A',  which  is  perpendicular  to  the  vertical  plane  (See  DA, 
Fig.  3),  it  will  describe  an  arc  parallel  to  the  vertical  plane  / 


Fio.  6.  Pis.  7. 

whose  vertical  projection,  m'o'm'",  will  be  an  equal  arc,  with 
centre  at  A',  and  its  horizontal  projection,  mom",  a  straight  line, 
parallel  to  the  ground  line. 

c — If  a  point  mm',  Fig. 
7,  which  is  vertically  over  a 
horizontal  axis,  A  B,  revolves 
90°,  it  will  appear,  as  at  m", 
on  a  perpendicular,  mm",  to 

AB,  and  equal  to  its  height  £ 

m'n  above  the  axis.  (16.) 
For  the  arc  of  its  revolution 
is  in  a  vertical  plane,  perpen- 
dicular to  AB,  and  its  hori- 
zontal projection  is  therefore 
straight,  and  perpendicular 
toAB.  /" 

Here  the  axis  is  m  the  / 

horizontal  plane.     If  it  had  ^m" 

been  merely  parallel  to  that  Fro<  a 

plane,  m'n  would  have  been  estimated  from  its  vertical  projec- 
tion, which  would  have  been  parallel  to  the  ground  line. 


8 


ELEMENTS   OF 


Like  results  would  be  true  for  a  revolution  about  an  axis  in,  01 
parallel  to  the  vertical  plane.  The  student  should  construct 
figures  to  represent  these  cases. 

d — If  a  point  mm'  not  vertically  over  an  axis,  AB,  in  the 
horizontal  plane,  be  revolved  about  that  axis,  into  that  plane, 
Fig.  8,  it  will  appear  at  a  perpendicular  distance,  km",  from 
that  axis,  equal  to  its  true  perpendicular  distance,  in  space,  from 
AB.  This  distance,  as  may  be  made  evident  by  the  simplest 
model,  will  be  the  hypothenuse  of  a  right-angled  triangle,  whose 

base  equals  mk,  and  whose 
altitude  equals  m'n,  which 
last  is  the  true  height  of  the 
point  itself  above  its  hori- 
zontal projection,  m  (16.) 

e — Similarly,  in  Fig.  9, 
the  axis,  CD— C'D',  is  pa- 
rallel to  the  vertical  plane, 

C — ri — ^ — D  at  a  perpendicular  distance 

from  it,  equal  to  Jik,  and  the 
point  mm'  is  revolved  about 
*m  it,  into  a  vertical  plane  con- 

taining   CD— C'D'.       Af- 
ter such  revolution,  mm'  will  appear  at  m"m'",  where  m'"ri, 
perpendicular  to  C'D',  is  equal  to  the  hypothenuse  of  a  right- 
angled  triangle,  whose  base  is  m'n',  and  altitude,  mh,  the  per- 
,  pendicular  distance  of  the 

horizontal  projection  of 
the  point  from  that  of  the 
axis,  or  from  the  vertical 
plane  through  the  axis. 

22.  These,  being  exam- 
ples of  the  main  principles 
and  operations  relating  to 
the  revolution  of  points, 
the  following  relates  to  the 
selection  of  new  planes  of 
projection. 

a — "When  it  is  desired  to 
represent  an  object  on  a 
plane  which  is  oblique  to  its  dimensions,  it  is  obviously  necessary 


MACHINE   CONSTRUCTION   AND   DRAWING. 


9 


to  begin  with  a  projection  made  on  a  plane  which  is  parallel 
to  two  of  its  dimensions.  Thus,  in  Fig.  10,  the  plane  ML  is 
vertical,  and  parallel  to  two  dimensions  of  the  rectangular 
block,  ad—a"d". 

b — The  principle  is  also  to  be  observed,  in  these  operations,  that 
any  number  of  different  elevations  of  the  same  point  are  at 
equal  heights  above  the  common  horizontal  plane.  Thus  a'b  is 
made  equal  to  a"c,  and  on  a  perpendicular  to  the  ground  line 
through  a  (19),  in  order  to  find  a',  the  projection  of  «,  on  that 
vertical  plane  whose  ground  line  is  GL. 

c — To  avoid  the  use  of  vertical  planes  which  are  oblique  to 
each  other,  as  they  are  in  Fig.  10,  conceive  the  body,  as  ad — a' 'd" , 
to  be  turned  horizontally  about  any  vertical  axis,  till  it  is 
brought  parallel  to  the  one  vertical  plane  used,  and  begin  with 
its  projections  in  that  position.  Thus,  in  Fig.  11,  after  making 


first  the  elevation,  a'b'e',  and  second  the  plan,  aba  j  third,  make 
the  new  plan,  ABC,  of  the  samejform  as  abc,  but  turned  to  re- 
present the  desired  position  of  the  body  relative  to  the  vertical 
plane  of  projection.  As  the  position  of  the  body,  relative  to 
the  horizontal  plane,  has  not  changed,  all  its  points  will  be  at 
the  same  height  as  before.  Therefore  any  point,  as  A',  of  the 
desired  elevation,  is  at  the  intersection  of  the  projecting  line 
A  A7,  perpendicular  to  the  ground  line,  GL,  with  the  line  #'A', 
which  is  parallel  to  the  ground  line. 


10 


ELEMENTS   OF 


Constructions  of  the  Ellipse. 

23.  It  not  nnfrequently  happens,  that  some  of  the  wheels  or 
circular  parts  of  a  machine  are  situated  in  planes  which  are 
oblique  to  each  other. 

All  such  parts,  when  oblique  to  the  plane  of  projection,  will 
be  projected  in  ellipses.  For  the  further  preliminary  informa- 
tion of  self -instructors,  especially,  some  convenient  constructions 
of  the  ellipse  are  therefore  added. 

24.  An  ellipse,  Fig.  12,  is  a  plane  curve,  such  that  the  sum 

of   the   distances,  as 

c  PF  +  PF',  from   (my 

point  of  the  circum- 
ference, to  the  fixed 
points  F,  F', within  the 
curve,  is  always  equal 
to  AB ;  the  longest 
line  within  the  curve, 
and  which  is  called 
the  transverse  axis. 
F  and  F'  are  called 
foci. 

The  middle  point, 
E,  of  the  transverse 

axis,  is  the  centre  of  the  curve,  and  bisects  every  line  drawn 
through  it  and  limited  by  the  curve.  Every  such  line  is  a 
diameter  of  the  curve.  The  shortest  diameter,  CD,  is  perpen- 
dicular to  AB,  and  is  called  the  conjugate  axis. 

25.  The  above  definition  affords  a  familiar  mechanical  con- 
struction of  the  ellipse  by  string  and  pencil,  the  string  being 
equal  in  length  to  AB,  and  fastened  at  F  and  F'.      Also  a  con- 
struction by  points,  with  dividers,  by   drawing  pairs  of  arcs 
from  F  and  F'  as  centres,  and  whose  radii,  taken  together,  shall 
equal  AB,  the  lesser  one  being  always  greater  than  AF.     Such 
arcs  will  intersect,  so  as  to  give  four  points  of  the  ellipse,  for 
each  pair  of  lines  taken  as  radii.     This  construction  is  not 
figured,  either  of  the  two  following  being  better  for  the  drafts- 
man's use. 

26.  To  construct  an  ellipse  by  radials  from  the  extremities 
of  the  axes. 


MACHINE   CONSTRUCTION    AND   DRAWING. 


11 


Let  AO  and  CO,  Fig.13,  be  the  given  semi-axes  of  an  ellipse. 
Make  AE  =  OC,  and  parallel  to  it.  Divide  AO  and  AE 
into  the  same  number  of 
equal  parts,  and  number 
them  as  in  the  figure. 
Then  lines  from  C  and  D, 
and  through  correspond- 
ing points  of  division, 
will  intersect  at  points, 
as  a,  I,  and  G  of  a  true 
ellipse.  The  other  three 
quarters  of  the  ellipse 
can  be  similarly  con- 
structed. 

It    would    have    been  Fia>13 

equally  correct    to    have 

equally  divided  CE  and  CO,  and  to  have  drawn  the  radial 
lines  through  the  points  of  division  and  from  the  opposite  ends 
of  the  transverse  axis. 


If  AE  were  made  equal  to  AO,  the  same  construction  would 


12  ELEMENTS   OF 

have  given  the  circle  of  which  the  ellipse  AC  is  really  the  ob- 
lique projection. 

27.  To  construct  an  ellipse,  by  concentric  circles  on  its  two 
axes. 

Let  AB  and  CD,  Fig.  14,  be  the  given  axes.  Describe  circles 
on  them  as  diameters,  as  shown.  Divide  the  circumferences  of 
these  circles  into  any  convenient  number  of  equal  parts,  and 
number  them  similarly,  as  shown.  Then,  parallels  to  AB, 
through  the  points  on  the  inner  circle,  will  intersect  perpendi- 
culars to  AB,  through  the  corresponding  points  of  the  outer 
circle,  at  points,  as  a  and  5,  of  a  true  ellipse,  whose  axes  are  AB 
and  CD. 

Special  Definitions. 

28.  A  MACHINE  is  an  assemblage  of  pieces,  attached  to  a  com- 
mon support,  and  acting  upon  each  other  to  produce  a  certain  re- 
sult ;  and  so  that  a  given  position  of  one  will  determine  that 
of  all  the  rest. 

29.  It  is  here  convenient  to  distinguish  the  terms:  "  Engine," 
"Machine,"  "Tool,"  and  "Instrument." 

An  engine,  and  a  machine,  are  not  essentially,  or  necessarily, 
different  things  ;  but  different  names  for  things  essentially  alike, 
and  expressive  of  different  ways  in  which  the  latter  may  be  re- 
garded. 

Thus,  from  the  etymology  of  the  terms,  engine — an 
invention — is  a  product  of  intelligence ;  and  machine 
— a  means — is  something  adapted,  as  a  cause,  to  a  certain 
end.  Hence,  therefore,  when  a  given  combination  of  working 
parts  is  generally  thought  of,  more  as  a  product  of  intelligence 
than  otherwise,  it  is  called  an  engine,  as  a  steam  engine,  or  a  di- 
viding engine.  But  when  the  same  is  thought  of  chiefly  in  re- 
gard to  the  end  for  which  it  is  made,  it  is  called  a  machine,  as 
a  spinning  machine.  Thus  any  piece  of  mechanism  may  be 
called  indifferently  an  engine  or  a  machine,  and  many  are  thus 
indifferently  termed,  as  locomotives  and  steam  fire  engines. 

30.  Instruments  are  distinguished  from  machines  in  being 
more  intimately  and  continuously  controlled  by  life  in  all  their 
movements.     Thus  an  organ  acts  only  when,  and  just  as,  it  is 
played  on  ;  and  the  like  is  true  of  engineering  instruments,  and 
to  a  great  extent,  of  mounted  telescopes,  since  so  many  of  their 


MACHINE   CONSTRUCTION  AND  DRAWING.  13 

parts  are  separately  adjustable  by  the  operator.  A  distinguishing 
feature  of  instruments,  then,  is  that  their  parts  are  separately 
movable. 

31.  Again :  tools  are  mainly  the  servants  of  manual  skill,  or 
training  in  processes  ;  instruments  are  servants  of  a  higher  or- 
der of  intelligence,  such  as  results  from  a  training  in  principles. 
Thus  we  say  "  the  tools  of  a  trade"  and  "  the  instruments  of 
a  profession  /"  a  carpenter's  tools,  but  an  engineer's  or  a  sur- 
geon's instruments. 

In  reference  to  their  material  uses,  tools  are  used  in  making 
the  machines  by  which  in  turn  consumable  products,  used  in 
common  life,  are  fabricated.  Thus  machine  shop  machines,  are 
often  called  "machine  tools"  or  "machinist's  tools"  while 
those  used  by  hand  are  called  hand  tools  or  bench  tools.  In 
these  the  train  of  pieces  forming  a  machine,  is  wanting ;  while 
in  machine  tools,  it  is  the  final  piece  acting  immediately  on  the 
work,  and  driven  by  a  machine,  rather  than  directly  by  hand, 
that  is  strictly  called  the  tool. 


Classification  of  Machines. 

32.  The  world  of  machinery  is  too  vast  and  varied  to  yield 
readily  to  attempts  to  classify  its  members.     Moreover,  the  com- 
ponents of  mechanism  need  to  be  differently  classified  for  mathe- 
matical and  for  descriptive  treatment. 

The  following  articles  present  an  outline  of  classification 
suited  to  the  subject  of  Descriptive  Mechanism. 

33.  The  immediate  source  of  the  power  which  moves  any  one 
or  more  machines,  is  some  form  of  prime  mover  in  which  some 
force  of  Nature,  as  muscular  power ;  the  weight  or  impact  of 
water ;  the  elasticity  of  springs,  or  of  expansive  vapor ;    or 
electrical  attraction,  is  made  available  for  producing  motion. 

The  first  grand  division  of  machines,  is,  therefore,  into  Mo- 
tors, or  Motive  Machines,  in  which  a  force  of  Nature  is  made  an 
available  power ;  and  Workers  or  Operative  Machines,  which 
perform  some  special  duty,  as  with  or  upon  raw  material,  by 
virtue  of  their  design. 

34.  Again :  some  machines  give  only  numerical  or  abstract 
or  intangible  results ;  signs  or  data,  rather  than  substantial  pro- 
ducts ;  while  others  do  produce  such  products. 


14  ELEMENTS   OF 

Hence  Operative  Machines  may  be  grouped  into  the  two 
divisions  of  Registrative,  and  Proactive  Machines. 

Here  it  is  important  to  explain  that  a  productive  machine 
does  not  necessarily  produce  a  finished  result,  but  if,  in  connec- 
tion with  others,  as  in  case  of  the  cotton  gin,  or  a  dredging  ma- 
chine, it  contributes  towards  such  a  result,  it  is  entitled  to  its 
name. 

35.  REGISTRATIVE  MACHINES  may  be  enumerated  as  follows: 
1°. — Counting  Machines  /  such  as  those  sometimes  attached 

to  steam  engines,*  or  turbines,  to  indicate  their  revolutions ;  or 
to  Burden's  horseshoe  machine,  or  Hoe's  power  presses,  to  re- 
gister their  production. 

2°. — Measuring  Machines  ;  of  time,  space,  motion,  mag- 
nitude, and  force,  as  timekeepers ;  "  Atwood's  machine" 
for  determining  the  laws  of  falling  bodies ;  water  and  gas  me- 
ters ;  dynamometers  and  pressure  gauges  ;  weighing  machines, 
etc. 

3°. — Copying  and  Drawing  Machines  ;  such  as  pantographs, 
elliptographs,  Olivier's  instruments  for  drawing  certain  curves,f 
and  ruling  machines. 

4°.   Calculating  Machines. 

5°. — Recording  Machines  /  as  telegraphic  machines  and  steam 
engine  indicators. 

36.  PRODUCTIVE  MACHINES.     These  modify  matter  only  in 
respect  to  its  position,  its  form,  and  its  dimensions  /  that  is, 
geometrically  &&&  physically  /  and  not  in  its  atomic  constitution, 
or  chemically.     We  have  then — 

I. — Machines  for  changing  the  POSITION  of  matter. 

1°. — By  simple  removal  by  stationary  machines,  as  by  cap- 
stans, windlasses,  cranes,  hoisting  machines,  derricks,  and  suc- 
tion pumps  of  all  kinds. 

2°. — By  conveyance,  whatever  the  direction  or  distance,  as  in 
"  rolling  stock  "  generally ;  and  the  moving  mechanism  of  "  at- 
mospheric despatch  "  apparatus,  common  road  engines,  etc. 

3°. — By  projection,  as  in  ancient,  or  mechanical,  and  modern, 
or  explosive  artillery ;  also  in  all  kinds  of  forcing  pumps,  the 
hydraulic  ram,  etc. 

*  "Engineering,"  voL  iv.,  p.  371. 

f  Olivier's  Des.  Geom.  and  Applications. 


MACHINE  CONSTRUCTION   AND   DRAWING.  15 

4°. — Ej  separation,  as  in  reaping,  ploughing,  digging,  dredg- 
ing, and  stumping  machines ;  in  fruit  paring,  fulling,  washing, 
and  churning  machines ;  in  machines  for  expressing  or  dispers- 
ing fluids  from  fruits  or  mixtures,  and  in  ginning,  threshing, 
and  smut  machines. 

5°. — By  distribution,  1st,  of  determinate  bodies,  as  in  pin- 
sticking,  wire-card  making,  type-setting,  pile-driving,  and  seed- 
planting  machines. 

2d,  of  matter  indefinitely,  as  in  elevators  and  blowing  en- 
gines. 

3d,  of  films  or  material  impressions,  as  in  printing  machines 
of  all  kinds,  upon  all  sorts  of  materials. 

6°. — By  uniting,  1st,  by  interlacing— first,  of  fibres,  as  in  felt- 
ing, paper-making,  carding,  roving,  and  spinning  machines ; 
second,  of  threads,  as  in  weaving  and  knitting  machines. 

2d.  By  union  of  particles,  as  in  mixing  machines. 

3d.  By  union  of  pieces,  as  in  sewing,  pegging,  and  ri  vetting 
machines. 

II. — Machines  for  changing  or  perfecting  the  FORM  of  matter : 

1st. — By  definite  division,  i.  e.,  into  definite  parts,  as  in  saw- 
ing, cutting,  shearing,  and  punching  machines. 

2d. — By  surface  abstraction  of  portions  of  indefinite  form,  as 
in  planing,  turning,  shaping,  milling,  boring,  polishing,  mor- 
tising, drilling,  slotting,  paring,  carving,  and  screw-cutting 
machines. 

3^. — By  moulding  pressure,  and  often,  or  always,  without  loss 
of  material ;  as  in  rolling,  forging,  squeezing,  wire-drawing, 
coining,  brick-making,  moulding,  bending,  folding,  and  swaging 
machines. 

III. — Machines  for  changing  the  DIMENSIONS  of  matter : 
1st. — By  condensation,  as  in  road-rolling  machines  and  presses 
for  compressing  matter. 

26?. — By  indefinite  division,  as  in  chopping,  tearing,  grind- 
ing, crushing,  and  stamping  machines. 


Functional  Classification  of  Mechanical  Organs. 

37.  The  foregoing  reconnoissance,  so  to  speak,  of  the  field  of 
mechanism  may  give  an  idea  of  its  extent,  and  may  direct  the 


16  ELEMENTS   OF 

student's  reading  and  practice.  But,  for  present  purposes,  it  is 
to  be  observed,  that  the  vast  range  of  mechanism  here  opened 
to  view  is  composed  mostly  of  endlessly  varied  combinations 
and  proportions  of  a  few  mechanical  elements  or  organs. 

The  drawing  of  the  separate  elements  or  organs  of  mechan- 
ism will  be  the  chief  subject  of  the  following  pages,  in  connec- 
tion with  so  much  description  of  their  successive  forms  in  pro- 
gressive practice,  and  of  their  action  and  use,  as  will  lend 
additional  interest  and  value  to  the  drawing  of  them. 

Some  instructions  upon  the  drawing  of  connected  trains  of 
mechanism  will  be  given  afterwards. 

38.  Mechanical  organs  may  be  conveniently  classified  as  fol- 
lows, according  to  their  functions,  into — 

Supporters,  Regulators, 

Receivers,  Modulators, 

Communicators,  Operators. 

39.  SUPPORTERS,  as  their  name  implies,  are  the  frames  or 
other  fixed  supporting  parts  of  machines,  whether  general  sup- 
ports of  the  whole  machine  or  local  ones  of  particular  parts. 

RECEIVERS  are  those  parts  to  which  the  motive  power  is  first 
applied  in  any  machine,  as  in  the  piston  of  a  steam  engine  or 
the  endless  platform  of  a  horse-power  machine. 

COMMUNICATORS  are  the  pieces  which  communicate  the  motion 
of  the  receiver  to  that  of  the  parts  which  act  on  the  material 
presented  to  the  machine. 

REGULATORS  are  those  organs  which  determine  the  effort 
exerted,  the  equalizing  of  its  expenditure,  or  the  supply  or  dis- 
charge of  engines,  etc. 

MODULATORS  are  organs  for  the  purpose  of  changing  the 
relations  of  motion,  as  by  reversing,  disengaging,  intermitting, 
etc.,  or  by  changing  the  ratio  of  the  velocities  of  connected 
pieces. 

OPERATORS  are  the  organs  which  act  directly  on  the  raw 
material,  or  to  immediately  accomplish  the  object  of  the  ma- 
chine. 

The  following  table  presents  a  more  detailed  view  of  these 
organs. 


TABLE. 


FUNCTIONAL  CLASSIFICATION  OF  MECHANICAL  ORGANS. 


18 


ELEMENTS    OF 


FUNCTIONAL  CLASSIFICATION. 

(Beds. 
Housing. 
Standards. 
Frames. 


L    SUFPOBTEBB 


Local. 


tt  EECEIVEBS. 


HI.    COianJNICATOB& 


Princvpai. 


Local  bed  plates. 
Brackets  and  arms. 
Pillow  blocks  and  axle  boxes. 
Bracket  and  suspension  hang- 
ers. 

Footsteps  and  bolsters. 
Face  plates. 
Travelling  tables. 
Guides  and  stuffing-boxes. 
Steam  cylinders. 
Pump  barrels. 
I.  Cases  or  chambers. 

Winches. 

Levers  of  horse  mills. 

Endless    platforms     of    horse 

powers. 

Driving  pulleys. 
Vertical  water-wheel  buckets. 
Turbine  buckets. 
Windmill  vanes. 

r  Pistons. 
reaprocattng  I -g^ 

1  Beam  levers,  as  of  hand  fire- 
l      engines. 
Bandwheels. 
Excentrics. 
Screws.  ( Racks. 

f  Spur  wheels,      -j  Circular,  el- 
j  Bevel  wheels.      (      liptic,  etc. 
L  Gears.  -<  Hyperboloidal 
I     wheels. 
^  Spiral  wheels. 


fin  circuit  motion. 


In 


Bands. 
Cords. 
Chains. 


Articulations. 


f  Fixed  couplings. 

Cranks. 

Rockers. 

Links. 

Working  beams. 

Jointed  rods,  etc. 
iHooke's  joint. 


MACHINE    CONSTRUCTION    AND    DRAWING. 


19 


IV.  REGULATORS. 


V.  MODULATOBS 


f  Low  water  detectors. 

!'  Giffard's  injector. 
Cocks. 
r  Slide.— Greene, 
v.  Valves •]  Puppet. — Putnam. 

(  Rotary.— Corliss. 

r  Of  st'm  pipe  f  Huntoon. 

opening.     ]  Snow. 
/  BalL  l  (  Judson. 

i  Governors.  •<  Fan.  f  4  . 

(Oil.    )    j  Of  st'm  v'lve  j  ( 
Flywheels.  L     °Penine      ( Corliss. 

f  Reversing  actions.     Band  shifters,  etc. 
I  Intermitting  actions.    Escapements,  etc. 
-j  Disengaging  actions.     Couplings,  etc. 
I  Speed  changers.     Cone  pulleys,  etc. 
t  Tool-holders,  and  slide  rests. 


Putnam. 


VI.  OPERATORS  . . 


f  Saws. 

I  Drills. 

\  Cutters. 

j  Paddle  wheels. 

{_  Screw  propellers. 


40.  It  should  here  be  noted  that  many  of  these  elements, 
especially  among  modulators  and  regulators,  are  compound 
organs,  or  sub-machines,  consisting  of  a  train  of  parts,  as  in 
Keversing  actions,  Slide  rests,  Escapements,  and  Governors. 

"We  therefore  define  a  sub-machine  to  be  a  series  of  con- 
nected pieces,  designed  to  perform  a  part  subservient  to  the  main 
object  of  the  machine  to  which  it  is  attached. 


Geometrical  Classification. 

41.  Though  the  foregoing  may  seem  an  elegant  classification 
of  the  elements  of  mechanism,  yet  it  is  partly  obscure ;  for  a 
given  element  does  not,  inherently  and  always,  belong  only  to 
one  and  the  same  class.  Thus  a  piston  as  a  receiver  in  a  steam 
engine  is  not  conspicuously,  if  always  at  all,  diiferent  from  a 
piston  as  an  operator  in  a  pump.  Also,  a  spur  wheel,  which  is 
usually  a  communicator,  becomes  an  operator  and  regulator, 
combined,  in  the  geared  fly  wheel  of  an  engine. 


Z(J  ELEMENTS    OF 

i  Still  the  foregoing  classification  is  generally  useful. 

42.  The  following,  which  is  new  and  entirely  different,   is 
combined   with  the  former  in  the  "general  table."     It  con- 
sists in  arranging  mechanical  elements  according  to  the  geo- 
metrical  magnitudes    which    express   their  essential  or  ideal 
character,  and  to  which  they  may  therefore  be  reduced. 

For  example,  a  shaft  revolving  in  two  pillow  blocks,  is  essen- 
tially a  line  supported  at  two  fixed  points.  Hence  a  pillow 
block  is  classified  as  a  mechanical  point.  Likewise,  material 
governor  halls  reduce,  in  thought,  to  heavy  points  at  which  their 
whole  action  is  concentrated. 

Other  elements,  which  act  by  virtue  of  their  surfaces,  or  are 
equivalent  to  certain  mutually  acting  surfaces,  are  classified 
according  to  their  surfaces.  Thus,  spur  wheels  are  equivalent 
to  rolling  cylinders,  etc.  By  following  out  this  idea,  the  classi- 
fication expressed  in  the  horizontal  columns  of  the  general 
table,  with  the  headings  at  the  left,  will  be  intelligible. 

43.  We  now  proceed  to  develope  the  foregoing  double  scheme 
<in  a  series  of  illustrations  of  the  several  classes  of  mechanical 
organs  there  named. 

These  illustrations  embrace,  primarily,  practical  examples, 
drawn  to  scale,  -in  a  series  of  plates  of  a  size  convenient  for 
adoption  in  actual  class  practice ;  and,  secondarily,  brief 
notices  and  simpler  illustrations,  of  various  other  forms  of  each 
of  the  organs  selected  as  examples. 

The  course,  thus  composed,  is  based  upon  the  idea  of  at  least 
one  good  representative  plate,  of  each  of  the  six  classes  of 
organs,  as  a  minimum  for  the  student's  practice  under  instruc- 
tion. But,  to  ensure  agreeable  variety,  as  well  as  material  to 
supply  the  wants '  of  more  rapid  workers,  several  examples, 
drawn  to  scale,  are  given  in  each  class  of  organs,  so  that  all 
the  members  of  a  class  need  not  necessarily  draw  the  same 
objects. 


Reduction  of  Scales. 

44.  Where  the  admirable  French  colored  mechanical  litho- 
graphs, or  suitable  actual  objects,  are  at  hand,  students,  so  far 
as  qualified,  may  profitably  make  drawings  from  them.  But 
in  drawing  from  the  French  plates,  those  should  principally  be 


MACHINE    CON6TKTJCTION   AND   DRAWING.  21 

chosen  which  give  a  scale  and  measurements,  and  the  copy 
should  be  drawn  from  the  measurements  to  a  new  scale. 

The  scales  given  on  the  originals,  being  in  French  measures, 
the  following  examples  will  illustrate  their  transformation  into 
suitable  English  measures. 

First,  scales  are  expressed  by  one  or  more  units  of  lower 
denomination  to  one  of  the  same  or  of  a  higher,  as  a  scale  of 
two  and  a  half  inches  to  one  inch  or  to  a  foot.  Suppose,  then, 
that  we  have  a  French  drawing  of  some  small  machine,  on  a 
scale  of  24  decimetres  to  1  metre. 

1  metre=39.4  inches,  very  nearly,  and  as  100  decimetres^! 
metre, 

1  decimetre =.394  inches,  very  nearly,  and 

24  decimetres =9. 45 6  inches,  or  a  scale  of  J,  very  nearly. 
Suppose,  then,  that  we  wish  a  scale  of  about  •£.  "We  see  that 
one  decimetre =f  of  an  inch,  very  nearly,  then  take  -|-  of  an  inch 
for  a  decimetre,  and  24  decimetres=S  inches  ;  that  is,  8  inches 
to  1  metre = a  scale  of  •£•  very  nearly. 

Second,  scales  are  expressed  in  terms  of  one  or  more  units  of 
higher  denomination  to  one  of  the  same  or  a  lower,  as  a  scale  of 
four  inches  to  an  inch— a  scale  of  J  ;  or  of  five  feet  to  one  inch 
=TV  Suppose,  then,  a  French  drawing,  on  a  scale  of  3  metres 
to  1  centimetre,  is  to  be  copied.  1  centimetre =3.94  inches, 
nearly  ;  and  one-third  of  this  on  the  scale=1.31  inches,  nearly, 
will  be  a  metre  of  a  scale,  giving  a  scale  of  about  ^  since  a 
metre =39.4  inches,  which  would  be  adapted  to  a  very  large 
machine,  with  the  smaller  parts  omitted.  To  enlarge  the  scale 
to  about  -^o,  construct  a  new  scale  in  which  2  inches  shall  be 
called  a  metre ;  then,  2  inches  to  39.4  inches  is  a  scale  of  ^ 
very  nearly. 

45.  "We  will  now  proceed  directly  with  the  explanation  of 
the  plates,  which  are  of  about  the  size  recommended  for  stu- 
dent practice,  viz. :  8£  x  12|-  inches,  that  is,  such  as  may  be  made 
by  dividing  a  sheet  of  super-ro}ral  drawing  paper,  stretched  upon 
the  board,  into  four  equal  plates. 

If  other  sizes  be  preferred,  we  would  recommend  imperial 
paper  in  four  plates  of  9£  x  13|  inches,  or  medium  paper  in 
two  plates  of  10  x  15  inches ;  but  that  all  the  plates  of  each  one's 
set  should  be  of  uniform  size. 


ELEMENTS   OF 


PAKT   II. 

THEOREMS,  PROBLEMS,  AND  EXAMPLES  ON  ELEMENTS 
OF  MACHINES. 

CLASS  L-SUPPORTERS. 

SECTION  I.— LOCAL  SUPPORTEES. 

46.  Local  supporters  are  very  various,  and  difficult  to  classify. 
The  following  partial  catalogue  may  therefore  serve  to  suggest 
other  kinds  and  forms  of  special  supports. 

Local  beds  /  as  those  of  especially  large  and  heavy  parts. 

Brackets  and  arms,  pillow-blocks,  axle-boxes,  bracket  and 
suspended  Jiangers  ;  supporters  of  horizontal  revolving  shafts. 

Footsteps  and  bolsters  /  supporters  of  vertical  revolving  shafts. 

Simple  tool-rests  or  holders  /  supporters  of  operating  tools. 

Simple  chucks  and  face-plates  to  support  revolving  material, 
as  in  common  and  wheel-turning  lathes. 

Travelling-tables  /  as  in  planing,  milling,  drilling,  and  shaping 
machines. 

Guides  and  stuffing-boxes  /  as  in  steam  engines. 

Cylinders,  barrels,  chambers,  chests,  etc.,  for  water,  steam,  air, 
etc. 

A— Point  Supporters. 

EXAMPLE  I. 
A  Heavy  Pillow-block. 

Dejmitions  and  description. — The  general  term,  " bearing" 
is  applied  to  the  supporting  surface  on  which  any  piece,  as  a 
revolving  shaft,  rests  ;  whatever  may  be  its  position.  The  piece 
which  supports  a  horizontal  revolving  shaft  is  called  a  pillow- 
block,  or  plumber-block,  when  itself  is  supported  from  below, 
and  open  at  both  ends  or  sides,  as  in  PI.  I.,  Figs.  1  and  2. 


MACHINE   CONSTRUCTION   AND   DRAWING.  23 

In  the  pillow-block,  PL  I,  Fig.  1,  there  is  the  body,  B,  and 
the  cover,  C.  The  part,  S,  of  the  body  is  the  sole,  through 
which,  as  at  ac,  holding-down-bolts  pass,  to  confine  the  block. 
bbf  are  brasses,  whose  inner  surfaces  are  cylindrical,  and  form 
the  bearings  for  a  shaft,.  They  are  flanged  so  as  to  prevent 
lateral  displacement,  and  are  therefore,  as  at  b,  dropped  into 
place  before  putting  on  the  cover  C.  That  part  of  the  shaft 
which  is  within  the  pillow-block  is  the  journal,  s  is  one  of  four 
set-screws  on  each  side  of  the  body,  to  set  up  the  side  brasses,  e, 
against  the  shaft.  Each  has  a  check-nut,  n.  At  A  are  the  nuts 
of  the  cover-bolts,  whose  heads,  not  shown,  are  in  recesses  in  the 
under  side  of  the  sole,  as  at  g,  PI.  II.,  Fig.  1.  The  bolt-holes, 
ac,  are  longer  one  way  than  the  other,  and  are  hence  said  to  be 
slotted.  They  are  thus  made  to  allow  the  position  of  the  block 
to  be  adjusted  between  the  lugs,  as  dd',  Fig.  5,  so  as  to  bring 
the  two  or  more  pillow-blocks  on  the  same  shaft  into  line ;  or, 
in  case  of  a  steam  engine,  to  adjust  the  distance  from  the  centre 
of  the  shaft  to  the  centre  of  the  cylinder. 

The  pillow-block  shown  in  the  figure,  being  for  a  14"  hori- 
zontal shaft,  the  bearings,  b,  are  continuous  only  in  the  lower 
half  of  the  block.  The  bolts,  as  A,  are  relieved  from  the  lateral 
pressure  of  the  shaft  upon  the  cover  by  forming  the  latter,  as 
shown,  to  be  embraced  between  the  walls,  B,  B,  of  the  body. 

This  pillow-block  was  designed  for  a  vertical  engine,  used  in 
driving  the  rolls  of  a  steel-rolling  mill.  At  the  beginning  there- 
fore of  the  down-stroke  of  the  piston,  the  cylinder  being  over- 
head, the  thrust  of  the  connecting-rod  and  crank,  and  the  weight 
of  the  14-inch  shaft,  come  upon  the  bottom  of  the  bearing  at  D. 
When  the  up-stroke  begins,  the  weight  of  these  three  pieces 
relieves  the  upward  thrust,  and  bars,  as  b',  afford  sufficient  bear- 
ing on  the  upper  side  of  the  shaft.  The  wear  being  mostly  at 
these  points,  provision  for  sufficient  adjustment  is  made  by  the 
space  between  the  cover  and  the  body  of  the  box. 

Construction. — From  the  above  description,  with  the  given 
scale  and  measurements,  the  drawing  can  be  made.  Observe 
that  each  elevation  has  a  centre  line,  and  that  the  plan,  which 
the  student  should  make,  with,  or  instead  of  one  of  the  eleva- 
tions, would  have  two  centre-lines.  A  section  should  also  be 
made. 

The  scale  might  well  be  increased  to  an  inch  and  a  half  to 
one  foot. 


24.  ELEMENTS   OF 

EXAMPLE  II. 
A  Putnam  Pillow-block. 

Description. — This  beautiful  pillow-block,  PI.  I.,  Fig.  2,  is 
not  shown  in  finished  drawings,  like  the  previous  figures,  but 
only  in  sketches,  with  measurements,  from  which  the  student 
can  make  finished  drawings. 

This  design  is  from  the  Putnam  Machine  Co.,  at  Fitchburg, 
Mass.,  and  is  adapted  to  a  horizontal  engine  of  about  24-horse 
power. 

In  a  horizontal  engine,  where  the  piston  is  at  either  end  of 
its  stroke,  the  connecting-rod  from  the  piston-rod  to  the  crank, 
and  the  crank,  a  short,  stout  arm  attached  to  the  shaft  by  which 
the  latter  is  revolved,  are  both  horizontal. 


c' 


Hence  when  the  connecting-rod  is  at  its  extreme  back  posi- 
tion, pc,  Fig.  15,  and  about  to  turn  forward,  it  acts  to  pull  the 
crank  CS  against  the  shaft  S,  and  the  latter  against  the  front 
of  its  bearing  in  the  pillow-block.  Likewise,  when  the  connect- 
ing-rod is  at  its  extreme  front  position,  p'c',  and  about  to  move 
backward,  it  acts  for  a  moment  to  push  the  crank  C'S,  and 
thence  the  shaft  S,  backward  against  the  pillow-block  bearing. 

Thus  the  pillow-block  of  a  horizontal  engine  is  mostly  worn 
at  the  points  A  and  B,  PI.  I.,  Fig.  2.  Separate  adjustable 
brasses  are  therefore  provided  at  those  points,  in  the  design  here 
shown.  A  recess,  abed,  contains  the  brass  ad,  and  wedge  be, 
each  ten  inches  long,  see  also  Fig.  3,  whose  tapering  faces  lie 
together  as  at  ef.  Hooked  bolts,  as  C,  enter  the  holes  gg'  in 
the  wedge.  By  turning  on  the  nuts,  A,  of  these  bolts — of  which 
there  are  four  in  all — the  bolts  and  wedges  are  drawn  up  and 
the  brasses  crowded  in  against  the  shaft.  Shallow  recesses,  as 
FG — F'G-',  in  other  parts  of  the  bearing,  are  filled  with  an  anti- 
friction alloy  called  Babbitt  metal,  and  the  wear  on  these  parts 
being  very  small,  the  cover,  H,  is  closely  fitted  to  the  body,  I, 
of  the  box.  The  collar  LL — I/I/  affords  a  long  bearing  for  the 
shaft. 


MACHINE   CONSTRUCTION   AND   DRAWING.  25 

The  sole,  holding-down-bolts,  and  cover-bolts,  will  be  recog- 
nized on  comparison  with  Fig.  1. 

Fig.  4  shows  a  sketch  of  the  manner  of  fastening  the  block 
to  the  top  flange,  AA,  of  the  bed-plate,  or  general  support  of 
the  engine,  by  means  of  a  key,  7ck',  through  the  holding-down 
bolt  bl>,  and  under  the  flange  AA.  In  Fig.  2,  MNN  shows 
the  plan  of  the  wider  part  of  this  flange,  on  which  the  pillow- 
block  rests. 

Construction. — Since  this  pillow-block  has  two  vertical  planes 
of  symmetry  through  its  centre,  O,  it  is  sufficient  to  show  the 
exterior  of  one  half  of  it.  In  the  elevation,  therefore,  all  to  the 
right  of  the  line  O'O",  is  a  section  on  the  plane  OR ;  and  in 
the  plan,  the  right-hand  half  shows  the  cover  removed.  The 
arcs,  as  nk  and  om,  are  drawn  from  O  as  a  centre.  The  points 
rr'j  ss',  and  tt'  are  fully  lettered,  as  the  large  and  small  curved 
outlines  of  the  block  in  their  neighborhood  sometimes  perplex 
learners. 

The  parts  on  which  shade  lines  are  scattered  in  the  elevation, 
are  sections  of  the  solid  portions  of  the  block,  which  is  hollow. 
In  the  finished  drawing,  these  portions  should,  of  course,  be  filled 
•\vith  fine  shade  lines,  omitting  the  bolt  holes,  as  K',  and  the 
bolt  C.  The  figure — 2 — is  a  sketch  from  a  model,  having  quite 
different  measurements  from  those  given.  It  will  therefore  be 
sufficient  for  the  student  to  give  the  same  views  as  in  Figs. 
2,  3,  and  4,  though  an  end  view,  partly  shown  in  the  right  hand 
one  of  Fig.  4,  might  usefully  be  completed  from  the  given 
measurements. 

47.  The  heavy  lines — or  lines  of  shade — are  shown  on  the 
principal  figures  of  this  plate.  Taken  in  connection  with 
the  fact  that  light  is  usually  so  taken  in  practical  examples, 
that  its  projections  make  angles  of  45  degrees  with  the  ground 
line,  and  the  principle  that  they  divide  surfaces  in  the  light 
from  those  in  the  dark,  they  will  assist  the  student  in  adding 
the  lines  of  shade  to  other  figures  where  they  are  not  shown. 


EXAMPLE  III. 
A  French  Pillow-Block. 
Description. — This  example,  PI.   II.,  Fig.  1,    is  given  on 


26  ELEMENTS   OF 

account  of  its  beauty  of  design,  rather  than  for  its  mechanical 
merits.  The  spherical  ends  of  the  nuts,  their  raised  seats,  f 
and  a;  the  tapered  collar,  FF',  the  three-centred  tops  of 
the  cover,  two  of  whose  centres  are  O  and  j?,  and  the  slight 
slope  of  the  surfaces  which  meet  at  oc — I'c',  all  give  a  fineness 
of  figure  which  pleases  the  eye.  But,  designed  for  a  horizontal 
engine,  as  it  is,  there  being  but  two  bolts  to  the  covers,  there  is 
no  provision  for  the  extra  wear  of  the  brasses  G,  at  the  lateral 
points  as  I ;  and  as  the  cover  does  not  slide  within  the  body  of 
the  block  as  in  Ex.  I.,  it  is  less  capable  of  resisting  the  hori- 
zontal thrust  upon  it. 

Construction. — This  block,  having  two  axes  of  symmetry, 
only  one-fourth  of  the  plan  is  shown.  The  scale  should  be 
increased  to  one-half,  or  three-fourths,  for  the  best  effect, 
and  half  of  the  plan  should  be  shown.  The  measurements  are 
left  to  be  found  by  the  given  scale,  or  assumed. 

The  end  elevation,  which  is  very  neat,  can  easily  be  made 
from  the  projections  here  shown ;  and  the  whole,  owing  to  its 
numerous  curved  and  oblique  surfaces,  would  be  a  particularly 
good  example  to  shade  with  graded  tints. 

Another  pillow-block,  which  may,  if  desired,  be  taken  as  a 
separate  example,  is  shown  at  MP — MP,  Figs.  1  and  2, 
PL  VII. 

EXAMPLE  IV. 
A  Locomotive  Main  Axle  Sox. 

Description. — PL  II.,  Fig.  2.  In  the  pillow-block,  the  shaft 
rests  in  the  block.  In  a  locomotive,  the  shaft  or  axle  is 
supported  by  the  wheels,  which,  in  turn,  rest  upon  the  rails  of 
the  track.  The  weight  of  the  engine  then  bears  upon  the  tops 
of  the  axle  boxes,  which,  again,  bear  down  upon  the  uppermost 
part  of  the  axles.  Hence  the  main  provisions  for  wear  and 
support  are  made  in  the  upper  part  of  the  box,  wrhich,  indeed,  is 
essentially  a  pillow  block  inverted,  and  modified  to  suit  the 
frame  of  the  engine. 

The  example  shown  is  from  recent  practice  on  the  ISTew 
York  Central  R.  R.  By  comparison  of  measurements  with 
those  of  the  engine  frame,  PL  VI.,  Figs.  3  and  4,  it  will  be  seen 
that  the  wedge  key,  W,  Fig.  3 ;  a'p,  Fig.  4,  is  between  the 
flanges  B, B— B'B"  of  the  box.  G  G,  G  is  the  body  of  the  box, 


MACHINE   CONSTRUCTION   AND   DRAWING.  27 

level  on  the  top  surfaces,  AA,  and  depressed  at  IIH, — H'  m  H'. 
The  depressions  SS — Sr — S"  are  the  seats  of  "  the  stirrup 
blocks,"  on  which,  through  the  medium  of  very  stout  springs, 
the  engine  rests. 

C  is  the  brass  lining,  made  thickest  at  E,  by  centring  its 
outer  curve  at  o,  %  an  inch  above  O,  the  centre  of  the  axle. 
e — e — e  are  recesses  for  Babbitt  metal.  KK  are  the  front  and 
rear  walls  of  the  oil  cellar,  which  is  packed  with  cotton  waste 
and  oil,  and  whose  lateral  walls,  L,  are  -^  of  an  inch  thick. 
The  outside  recess,  FF',  in  the  cellar,  keeps  the  bolt  cd,  which 
passes  through  the  front  and  rear  walls  to  hold  the  cellar  in 
place,  from  passing  through  the  oil. 

Construction. — The  titles  of  the  separate  views,  and  the 
given  traces  of  the  planes  of  section  used,  and  the  given 
measurements,  leave  little  need  for  minute  directions  here. 
The  scale  may  be  changed  to  £  or  £,  and  a  horizontal  section 
through  O  might  well  be  made.  It  is  left  for  the  student 
to  determine,  by  comparison  of  the  different  views,  which 
parts  of  the  sections  should  be  filled  with  lines  of  shading, 
as  being  in  the  planes  of  section. 


Shaft-Hangers. 

48.  On  entering  any  mechanical  establishment,  a  noticeable 
feature  consists  in  the  many  band  wheels,  revolving  on  a  com- 
mon axis,  or  "  line  of  shafting"  supported  from  the  walls  or 
ceiling ;  or  from  posts.  The  band  wheels  go  by  the  name  of 
"  overhead  pulleys?  and  their  supports  by  the  general  name  of 
hangers,  though  this  name  may  be  more  strictly  applied  to  sup- 
ports from  the  ceiling  timbers. 

Now  a  wall,  or  row  of  posts,  or  ceiling  timbers,  are  liable  to 
warp,  or  spring,  lean  or  settle,  and  thence  to  throw  any  bear- 
ings attached  to  them  out  of  line  with  each  other,  and  thus  to 
produce  an  injurious  binding  of  the  shafting  in  its  bearings. 
Again,  overhead  shafting  is  less  accessible  for  oiling  than  that 
which  is  near  the  floor ;  and,  if  unprotected,  may  drip  black- 
ened oil  disagreeably  upon  persons  and  things  below. 

Hence,  the  main  points  of  a  good  hanger  are,  first :  that  it 
shall  be  adjustable  both  vertically  and  horizontally,  so  that  its 
bearing  shall  be  in  line  with  all  the  others  of  the  same  row; 


28  ELEMENTS    OF 

second,  that  it  shall  seldom  require  oiling;  and  third,  that  it 
shall  not  drip. 

PL  III.,  Figs.  1  and  2  represent  two  very  good  hangers,  the 
second  of  which  fulfils  all  the  conditions  just  mentioned,  while 
both  are  good  exercises  in  the  construction  and  reading  of 
drawings. 

EXAMPLE   Y. 
A  Bracket  Hanger. 

Description. — PI.  III.,  Fig.  1.  This  design  is  from  the  Indus- 
trial Works  at  Philadelphia,  and  as  made  in  1858  and  sub- 
sequently. 

It  is  shown  in  two  complete  elevations  and  a  plan,  from  which 
the  bearing  is  removed ;  and  a  horizontal  section  through  the 
case  F,F',F"  is  shown. 

A, A', A"  is  the  bracket,  fastened  by  bolts,  at  bfi ft" ,  to  the 
wall.  A  two-inch  shaft  is  supported  at  C',C"D",  and  the  box 
C"D"  is  self -adjustable  by  its  spherical  curvature  shown  in 
dotted  lines,  where  it  passes  through  the  close-fitting  ring, 
B',B" ;  the  upper  and  lower  parts  of  which  are  held  together 
by  bolts  as  at  c',c".  At  d'd"  is  the  oil  hole  ;  e",e"  are  dripping 
cups  to  catch  any  oil  that  may  work  out  at  the  ends  of  the  bear- 
ing. They  rest  in  the  ears  or  recesses  at  e,e' .  The  ring  B'jB", 
is  attached  to  the  screw  S,S',S",  which  affords  a  vertical  adjust- 
ment to  the  bearing.  The  latter  is  adjusted  horizontally  by  the 
three  screws  m,  which  bear  against  the  hollow  cylinder  p, 
within  which  the  screw  S  works.  Just  above  the  letter  S  is 
seen  half  a  thread  of  this  screw.  The  shape  of  the  chamber, 
F,  allows  for  horizontal  adjustment,"  principally  in  a  direction 
perpendicular  to  the  wall,  to  which  the  bracket  is  fastened,  as  is 
obviously  most  necessary.  The  w^hole  being  adjusted,  the  check 
nuts  n,ri  and  N,N'  hold  the  bearing  fast  in  the  desired  position. 
Construction.— -The  measurements  not  given,  may  be  deter- 
mined by  the  scale,  or  may  be  assumed.  The  student  may  ad- 
vantageously increase  the  scale  to  one  fourth,  one  fifth*,  or  one 
sixth  ;  and  may  make  out  a  vertical  section  through  the  axis  of 
the  shaft. 

The  heavy  lines  are  indicated  by  small  double  marks  across 
them.  The  student  should,  however,  always  note  the  heavy 


MACHINE   CONSTRUCTION   AND   DRAWING.  29 

lines  for  himself  before  calling  for  assistance ;  guiding  himself 
by  the  principle  that  the  light  is  taken  so  that  its  projections 
make  angles  of  45  °  with  the  ground  line  ;  and  then  that  sur- 
faces illuminated  are  separated  from  those  in  the  dark  by  heavy 
lines.  (47,  Ex.  II.) 

EXAMPLE  VI. 
A  Self -Oiling  Drop-Hanger. 

Description. — PL  III.,  Figs.  2, 3.  This  design  is  from  Messrs. 
Bullard  and  Parsons,  Hartford,  Conn.  It  is  claimed  for  it  that 
it  requires  oiling  but  twice  a  year,  thus  saving  more  than  half 
of  the  oil,  and  nearly  all  the  labor  required  by  a  plain  box. 

A,  A'  is  the  top  plate,  solid  with  the  drop,  which  extends  in 
one  piece  to  the  line  Mm'.  The  moulded  cylindrical  part 
MM/V,  is  hollow,  and  receives  the  swivel  A'MM'w',  whose  bear- 
ings are  as  indicated  at  M  and  M,  the  space  between  the  lines 
V  and  G'  being  hollow  all  around.  The  swivel  also  is  hollow 
between  a'  and  a'",  from  MR  to  ~k'  /  the  ring  QQ',  being  in  one 
piece  with  the  swivel.  Fig.  3  shows  an  end  view  of  the  ring 
and  swivel,  where  O"O'V  is  the  form  of  a  section  of  the  ring  at 
the  top,  and  the  similar  small  figure  at  v"  is  a  section  at  the  bot- 
tom. By  means  of  the  nut  N,  working  through  the  head  of  the 
swivel,  the  latter  may  be  raised  or  lowered,  and  turned  in  any 
direction.  The  journal  box  itself,  gs — q't'  is  held  in  position 
within  the  ring  by  the  opposite  set  screws  n,n',n",  which  adjust 
it  laterally,  and  work  through  bearings  t,t,  not  shown  in  plan. 
The  box  being  thus  held  at  two  points  is  self-adjusting  to  imper- 
fections in  the  straight  line  of  the  shafting.  I/  is  the  oil  cellar, 
the  spiral  grooves,  L,L,  in  which,  hold  oiled  packing,  which  draws 
up  the  oil  from  L  by  capillary  attraction ;  and  the  circular  chan- 
nels at  q  and  g  catch  any  oil  that  might  otherwise  drip  out. 

In  reading  this  drawing,  we  notice  a  set  of  circles  with  Y  as 
a  centre  in  the  plan,  and  another,  with  X  as  a  centre  in  the  ele- 
vation. Of  the  former,  «,5,A,c  and  d,  with  a'fi'Ji'^c'  and  d',  re- 
present the  several  vertical  inner  and  outer  cylindrical  surfaces 
of  the  drop  and  swivel,  and  e— -f,  is  the  plan  of  the  extreme  cir- 
cumferences at  e'  andy.  Of  the  latter,  the  letters  of  reference 
show  the  position,  being  the  same  on  the  two  projections  of  the 
same  circle,  as  r — /,  the  end  circle  of  the  box ;  or  the  same 
cylindrical  surface,  as  pp',  the  inner  surface  of  the  box. 


30  ELEMENTS    OF 

The  letters  CO',  etc.,  and  HIT,  etc.,  clearly  indicate  the  form 
of  horizontal  sections  of  the  drop  and  the  ring. 

To  avoid  the  indistinctness  of  too  many  dotted  lines,  the  plan, 
HQ,  of  the  ring  is  made  in  full  lines. 

Construction. — The  measurements  not  given  may  be  ascer- 
tained by  a  scale,  or  suitably  assumed.  By  placing  the  figure 
lengthwise  on  the  plate,  the  scale  may  properly  be  enlarged  to 
one-third,  or  one-half. 


EXAMPLE  VII. 
Turbine  and  Spindle  Foot-Steps. 

Description. — A  foot-step  is  the  support  of  a  vertical  revolv- 
ing shaft  at  its  lower  extremity.  PL  II.,  Fig.  3,  represents  the 
footstep  for  a  Jonval  Turbine,  substantially  as  made  by  Col- 
lins and  Co.,  of  Norwich,  Conn.  SS — S'  is  the  bridge  tree,  ex- 
tending across  the  wheel  case  at  the  bottom,  and  stiffened  by  the 
rib  RR'.  The  socket,  dd—d'd',  is  solid  with  the  bridge  tree, 
and  surrounds  the  cup,  ab — a'b ',  whose  position  is  adjusted  by 
set  screws,  as  pp',  roughly  shown.  The  remaining  parts  are 
not  shown  in  the  plan.  B,  the  step  itself,  is  of  lignum  vitse, 
immovable  in  the  cup  ab — a'b'.  On  it  rests  the  step  bowl,  CD, 
of  iron,  which  is  keyed  to  the  shaft,  E,  of  the  wheel,  as  seen 
at  k,  and  is  solid  with  the  lower  plate  of  the  wheel. 

Construction. — The  measurements  may  be  determined  from 
the  scale,  and  recorded.  The  cup,  and  parts  above  it,  are  shown 
in  section,  and  may  be  shaded  accordingly.  Also  the  elevation 
is  shown  in  section,  as  cut  by  a  plane  a  little  in  front  of  RE. 

The  spindle  foot-step,  PL  II.,  Fig.  4,  gives  a  very  simple 
drawing  exercise,  but  is  noticed  on  account  of  its  utility.  Where 
thousands  of  spindles  are  running  in  the  same  mill,  any  device 
which  lessens  the  frequency  of  oiling  is  valuable.  In  this  foot- 
step, any  convenient  fibrous  packing  is  placed  in  the  annular 
space,  DD',  and  well  saturated  with  oil.  Openings,  aa,'  and  bb' ', 
conduct  the  oil  from  this  space  to  the  vertical  revolving  spindle, 
which  rests  in  the  step  CC'.  Near  the  upper  end,  the  spindle  is 
supported  by  another  bearing,  similar  to  A/'B",  but  open  at  both 
ends,  and  called  a  bolster. 

A  spindle  making  4,500  revolutions  per  minute  needs  oiling 


MACHINE   CONSTRUCTION   AND   DRAWING.  31 

not  oftener  than  twice  a  week  with  this  foot-step  and  bolster,  in- 
stead of  once  or  more  every  day. 

There  is  a  somewhat  similar  device,  but  without  the  fibrous 
packing,  known  as  Oilman's  spindle  step  for  "  Koving  Frames." 
These  machines  act  in  an  earlier  stage  of  the  formation  of  the 
thread,  and  their  spindles  revolve  more  slowly,  or  at  500  revolu- 
tions per  minute.  These  steps  require  oiling  but  three  or  four 
times  a  year. 

49.  In  leaving  the  subject  of  shaft  supports,  an  improvement 
in  the  shafting  itself  may  be  mentioned.  This  is  what  is  Known 
as  cold  Tolled  shafting.  Merchant,  and  other  manufactured  iron 
is  generally  rolled  hot;  but,  by  a  patent  process,  bars,  rods, 
axles,  also  plates  and  sheets,  are  now  rolled  cold.  This,  as  ex- 
periments show,  compresses,  hardens,  and  strengthens  the  iron ; 
and  also  leaves  it  highly  polished,  and  perfectly  true  in  straight- 
ness  and  roundness,  and  firmest  in  its  outer  surface  or  " skm" 
which  is  cut  away  in  other  shafting,  by  the  process  of  turning 
it  true  in  the  lathe. 

B — Line  Supporters. 

EXAMPLE  VIII. 
locomotive  Guide  Bars  and  Cross-head. 

Description. — The  outer  end  of  the  piston-rod  of  most  en- 
gines is  attached  to  a  block,  or  transverse  piece,  which  slides 
back  and  forth  as  constrained  by  fixed  guides,  upon  which  it 
moves.  The  block»or  transverse  piece  is  called  a  cross-head. 

When  the  guide  bars  are  separated  only  by  the  cross-head 
they  are,  ideally,  one  to  four  straight  and  parallel  lines,  on  or 
between  which  the  cross-head,  reduced  to  a  point,  moves.  When, 
as  in  side-lever,  and  some  other  engines,  they  are  necessarily 
separated  by  the  diameter  of  the  cylinder,  the  cross-head  becomes 
extended  into  a  transverse  line,  attached  to  the  piston-rod  at  its 
middle  point,  and  having  its  rectilinear  movement  determined, 
at  its  extreme  points,  by  the  guides. 

On  some  accounts,  the  cross-head  might  be  classed  with  com- 
municators, but  it  is  so  convenient  to  represent  it  in  place,  as 
working  between  its  guides,  that  it  is  here  accounted  a  supporter, 
which  indeed  it  is,  to  one  end  of  the  connecting  rod,  which 
actuates  the  crank,  and  thence  the  main  shaft  of  the  engine. 


ELEMENTS    OF 


PI.  II.,  Fig.  5.  T,T'  is  a  collar  on  the  back  end  of  the  cylin- 
der, from  which  project  the  pieces,  one  of  which  is  E,  to  which 
the  front  ends  of  the  guide  bare  are  bolted.  DD'  is  an  arm, 
open  like  a  loop  or  ring,  or  like  an  ox-bow,  at  the  part  to  which 
the  guides  are  fastened,  so  as  to  allow  the  vertical  play  of  the 
connecting  rod.  Here  the  pieces  E',  to  which  the  guides  are 
bolted,  are  themselves  bolted  to  DD'  by  the  nuts  and  bolts  at 
NN'  and  nN'.  Now,  BB'  is  the  front  upper  guide,  B,C'  the 
front  lower  one  ;  A,B'  the  back  upper  one,  and  A,C'  the  back 
lower* one.  That  is  B,  for  example,  is  the  horizontal  projection 
of  two  bars,  one  vertically  under  the  other ;  and  C',  for  example, 
is  the  vertical  projection  of  two,  one  of  which  is  exactly  behind 
the  other.  KR'R"  is  a  portion  of  the  piston-rod,  whose  full 
diameter  is  shown  in  the  elevation,  by  nicking  out  a  little  of  the 
guide  bars,  as  shown. 

The  cross-head,  which  is  quite  an  irregular  solid,  is  shown  in 
plan  and  elevation,  partly  hidden  by  the  guides ;  alone,  in  rear 
elevation,  in  Fig.  6  ;  and  wTith  a  cross  section  of  the  guides  and 
brasses  in  Fig.  7.  M,M',M"  is  the  body  of  the  cross-head,  flush 
with  the  tops  of  the  upper  guides,  and  the  under  surfaces  of  the 
lower  guides,  but  entirely  hidden  in  the  side  elevation.  W,  V V 
are  the  vertical  wings  of  the  cross-head,  giving  it  a  longer  bearing 
on  the  inner  faces  of  the  bars.  H,H',II",H'"  are  the  horizontal 
wings,  which  in  some  engines  are  as  thick  as  the  space  between 
the  upper  and  lower  bars.  In  this  design,  brasses  bfi'b ',l"b'' ', 
shown  also  in  section  above  and  below  II"',  intervene  between 
the  wings  H,H',  and  the  bars.  They  cannot  slip  out  to  right  or 
left,  being  hooked  at  both  ends,  as  shown  at  b'  on  the  lower  one. 
They  are  otherwise  confined  by  the  plate  FF',  which  is  bolted  to 
the  wing  H,H'.  The  back  end  of  the  piston-rod  is  conical,  and 
goes  through  the  body  of  the  cross-head,  as  shown  by  dotted 
lines.  It  is  fastened  by  the  key  M'k"k'".  The  pin  PP'  is 
cylindrical,  and  forms  a  point  of  attachment  for  the  connecting 
rod.  K,K"  is  an  arm,  projecting  from  the  back  plate  G,  to 
carry  the  pump-rod  L. 

Fig.  7  shows  a  section  of  the  back  bars,  brasses  and  wing  in 
the  plane  Y?/  /  and  a  section  of  the  front  bars  in  any  plane,  as 
X«,  to  the  right  of  the  brasses. 

Construction. — "With  this  description,  and  with  the  full 
measurements  and  lettering  of  parts  broken  away,  the  construc- 
tion can  readily  be  made.  The  scale  may  well  be  increased  to 


MACHINE   CONSTRUCTION   AND   DRAWING.  33. 

one-sixth,  or  even  one-fifth  ;  in  the  latter  case  by  breaking  out  a 
part  of  the  length  of  the  guides. 

50.  As  an  example  of  the  gradual  development  of  a  mechani- 
cal idea,  it  is  interesting  to  note  the  successive  forms  of  loco- 
motive  cross-heads  that  have   appeared.     Fig.    8   represents, 
roughly,  the  general  form  of  a  cross-head  often  seen  from  about 
1845   and   onward.      Here  the  single  guide  bar,  B,   running 
through  the  cross-head,  the  latter  has  the  greatest  leverage  for 
working  itself  in  a  rotary  direction  around  B.     The  piston-rod 
was  inserted  at  R,  and  P  is  the  end  of  the  pin  to  which  the  con- 
necting rod  was  attached  between  two  ears,  one  of  which  is  Q. 

Fig.  9  represents  an  improvement  relative  to  steadiness  of 
motion  in  the  cross-head  II,  by  making  it  move  on  two  guide 
bars,  B,B.  Here,  too,  we  have  an  elementary  illustration  of 
unessential  variations  of  one  idea,  for  the  guides  were  sometimes 
of  circular  section  instead  of  a  square  one ;  and  square  section 
guides  were  sometimes  set  diagonally,  or  so  that  opposite  edges 
as  aa  should  be  in  a  vertical  plane.  This  form  was  common 
between  1850  and  1860. 

Finally,  the  last  example,  Figs.  5-7,  represents  the  fully  de- 
veloped idea  of  steadying  the  cross-head  to  the  utmost,  by  confin- 
ing it  between  four  exterior  guide  bars ;  which  is  the  extreme 
opposite  in  effect  of  the  form  shown  in  Fig.  8.  This  form  has 
prevailed  in  the  United  States  since  about  1860,  especially  on 
"  outside  cylinder  "  engines. 

Where  there  is  a  greater  tendency  to  a  vertical  than  a  hori- 
zontal displacement  of  the  cross-head,  as  in  the  common  four- 
driver  switching  engines,  without  trucks,  which  rock  vertically 
a  good  deal,  the  guides  now  often  consist  of  two  bars  in  a  verti- 
cal plane,  with  a  cross-head  of  greatest  width  vertically  /  as  if 
the  plan  in  Fig.  5  was  an  elevation  of  guides  consisting  of  only 
two  bars. 

C— SURFACE  SUPPORTERS, 
a — Plane  Supporters. 

51.  Passing  these  without  figured   illustration,  we  merely 
define  iron-planer  tables  and  face  plates  of  lathes  as  movable 
supporters.     Each  is  pierced  with  many  cross-shaped  openings 
to  allow  large  or  small  work  to  be  conveniently  fastened  at  any 
point  of  it. 

3 


34  ELEMENTS   OF 


b — Developable  Supporters. 

52.  Associating  prismatic  and  pyramidal  forms  with  cylin- 
drical and  conical  ones,  we  distinguish  surface  from  volume 
elements,  when  it  is  only  the  surface  of  the  supporter,  and  not  its 
interior  capacity,  which  we  have  to  consider. 


EXAMPLE   IX. 
A  Local  Bed  Plate. 

Description. — PI.  I.,  Fig.  5,  represents  the  bed  for  a  60-ton  fly 
wheel,  at  the  Bessemer  steel  rolling  mill,  in  Troy,  1ST.  T.  Its 
principal  parts  are  the  sole,  AA' ;  the  vertical  web,  B — B'B' ; 
the  top  plate,  C,C' ;  the  gussets,  DD',  and  EE' ;  and  the  trans- 
verse supports,  as  FF',  through  which  the  holding-down  bolts 
pass  into  the  masonry  below. 

Both  projections  have  a  transverse  centre  line,  OO'.  The 
part  of  the  plan  to  the  right  of  the  broken  edge,  ab,  shows  a 
horizontal  section  in  the  plane,  MN" ;  dd'  is  one  of  two  lugs  to 
confine  the  pillow  block  which  rests  on  the  plate  CO'. 

Construction. — With  the  given  measurements,  sufficient  data 
are  afforded  for  drawing  this  bed,  as  shown,  or  with  the  substi- 
tution of  an  end  elevation,  and  longitudinal  and  transverse  sec- 
tions ;  some  one  or  more  of  which  variations  from  the  given 
figure  should  be  made  by  the  student. 


D— VOLUME  SUPPORTERS. 

EXAMPLE  X. 
A  Locomotive  Cylinder. 

Description. — PI.  IY.,  Fig.  1.  This  example  is  from  a  first- 
class  engine  of  the  New  York  Central  K.R,  taken  from  working 
drawings  of  an  engine  not  then  built. 

The  drawing  shows  an  end  elevation,  with  the  cylinder  head 
removed,  and  a  vertical  longitudinal  section. 

The  end  elevation  also  shows  a  part  of  the  saddle,  EFLF,  ex- 


MACHINE   CONSTRUCTION   AND   DRAWING.  35 

tending  across  the  engine,  and  bolted  to  the  smoke-box,  uv, 
while  the  cylinder  flanges,  S JD,  and  MN",  are  bolted,  the  former 
to  the  smoke-box,  and  the  latter  through  the  main  frame,  whose 
section  is  I,  to  the  end,  LH,  of  the  saddle. 

The  drawing  further  shows,  incidentally,  for  convenience,  a 
bottom  plan,  T  ;  a  transverse  section,  T"  ;  and  longitudinal  sec- 
tion, T",  of  the  steam  valve;  the  piston,  P,  with  its  rod,  E; 
and  the  stuffing-box,  UYw  ;  consisting  of  the  collar,  U,  of  the 
back  cylinder  head  ;  the  gland  Y,  bolted  to  U ;  and  the  annu- 
lar space,  w,  in  which  the  steam-tight  packing  is  confined  by  the 
gland,  Y,  and  ring  or  lining,  x. 

For  the  rest,  the  correspondence  of  the  letters  well  shows  the 
different  projections  of  the  same  parts.  Thus,  g'g" — gt,  is  the 
valve  seat ;  h'h,  indicating  lines  by  one  point,  is  the  floor  of  the 
steam-chest,  whose  sides  and  top  are  removed,  and  into  which 
steam  enters  through  a  pipe  behind  K'K  at  D',  and  the  port 
d",  which  may  be  12"  to  14"  long.  The  annular  surface,  of  the 
width,  j'l'— -j"l,  is  on  the  cylinder  head,  and  is  set  a  little  back 
from  I'm' — In"  to  allow  a  ring  of  packing  to  be  inserted. 
~Yy'y"n' — nmky  is  a  steam-port,  extending,  as  the  end  view  thus 
shows,  through  nearly  a  third  of  the  circumference  of  the 
cylinder,  at  each  end ;  C' — CC",  is  the  axis  of  the  cylinder, 
G'o'  the  radius  of  its  lore,  and  the  minutely  greater  distance, 
G'j)',  is  that  of  the  counter-bore  for  a  short  distance  at  each 
end,  as  shown  at  op,  and  intended  to  facilitate  the  discharge  of 
water  of  condensation.  BW  is  the  front  cylinder  cover  which, 
like  the  rear  one,  is  a  little  concave,  so  as  to  conform  to  the 
piston,  and  thus  reduce  the  volume  of  old  steam  left  in  the 
cylinder  at  the  beginning  of  a  new  stroke.  XXX  is  the  front 
cylinder-jacket  of  brass,  the  confined  air  within  which  keeps 
the  heat  of  the  cylinder  from  escaping,  and  is  ornamental. 

In  view  of  a  prevailing  disposition  in  some  quarters  to  strip 
the  locomotive  of  all  its  ornaments,  it  is  not  an  improper  di- 
gression to  say,  here,  that  it  is  probably  all  a  mistake  to  do  so. 
It  is  not  for  the  sake  of  the  engine,  though  that,  as  a  thing 
quite  analogous  to  life,  deserves  ornament,  nor  for  the  sake  of 
the  public  only,  nor  in  regard  to  the  character  of  the  train,  as 
express,  or  freight,  that  an  engine  is  to  be  ornamented ;  but  it  is 
chiefly  for  the  sake  of  the  men  who  operate  it.  If  $300  to  $500 
apiece,  spent  in  beautifying  the  passenger  engines,  and  $200  to 
$300,  each,  on  the  freight  engines,  interests  and  rationally 


36  ELEMENTS    OF 

gratifies  their  operators,  and  so  raises  the  morals  of  the  entire 
force  of  a  road  ;  it  is  money  well  spent.  It  may  be  true,  how- 
ever, that  brass  and  scarlet  are  not  the  chief  means  of  locomo- 
tive decoration.  An  abundance  of  smoothly  rounded  and 
finished  surfaces  of  iron  and  steel  may  have  a  greater  as  well 
as  more  quiet  elegance. 

Construction. — "With  the  full  measurements  given,  this  needs 
no  special  explanation.  By  turning  the  figures  crosswise  of  the 
plate,  and  substituting  a  mixed  plan  and  horizontal  section  for 
the  end  view,  the  scale  could  well  be  increased  to  one-sixth. 


EXAMPLE  XI. 
A  Jet  Condenser. 

General  explanations. — Steam  engines  are  distinguished,  in 
one  of  many  ways,  as  condensing,  or  non-condensing  j  popularly 
called,  low  and  high  pressure,  respectively. 

The  latter  terms  are  quite  loose,  since  there  is  no  particular 
point  at  which  pressure  may  be  said  to  cease  to  be  low  and  be- 
come high. 

High  pressure  engines  work  against  the  pressure  of  the  air, 
since  their  passages  for  the  escape  of  steam  from  the  cylinder 
open  into  the  atmosphere ;  while  the  cylinder,  acting  as  an  air- 
pump,  tends  to  exhaust  all  the  air  from  the  boiler,  so  that  there 
shall  be  only  steam  on  the  side  of  the  piston  which  is  at  the 
moment  open  to  the  boiler. 

Low  pressure  engines,  on  the  contrary,  have  a  vacuum  more 
or  less  perfect  on  the  opposite  side  of  the  piston  from  the  steam. 
Hence,  with  any  given  pressure,  they  have  an  advantage  of 
about  14  pounds  per  square  inch  over  high  pressure  engines. 

In  short,  each  has  steam,  only,  on  one  side  of  the  piston ; 
while  the  high  pressure  engine  has  an  opposing  atmosphere, 
but  the  low  pressure  one  a  vacuum,  on  the  opposite  side. 

The  vacuum,  maintained  in  the  low  pressure  engine,  exists 
primarily  in  the  condenser ;  a  vessel  immediately  communicat- 
ing with  the  steam-cylinder,  and  into  which  the  steam  passes 
after  effecting  a  stroke  of  the  steam-piston,  and  is  condensed. 

This  vacuum  is  produced  at  first  by  the  action  of  an  air-pump, 
which  is  a  part  of  the  engine,  and  which  removes  not  only  the 
air  at  first  found  in  the  condenser,  but  the  water  of  coudensa- 


MACHINE   CONSTRUCTION   AND   DRAWING.  37 

tion  also.  It  is  maintained  by  the  air-pump  and  by  the  process 
of  condensation  itself. 

There  are  two  classes  of  condensers,  according  as  the  escaped 
steam  is  brought  into  direct,  or  indirect  contact  with  cold  water 
as  a  means  of  condensation.  The  former  are  called  ^-conden- 
sers, the  latter,  surface-condensers. 

Description. — PL  Y.,  Figs.  1,  2,  3,  represents  a  jet-condenser 
of  the  form  frequently  found  on  American  lake  and  river 
boats.  Fig.  1  is  a  partial  plan  ;  Fig.  2  a  vertical  section  on  the 
vertical  plane  Mw,  Fig.  1 ;  and  Fig.  3  is  a  partial  elevation,  look- 
ing in  the  direction  indicated  on  Fig.  1  by  wM. 

MM — M'N' — M"N"  is  the  wall  of  the  condenser,  which  ie 
vertical  and  cylindrical.  AB — A'B — 'B"  is  the  injection-pipe , 
conducting  cold  water  to  the  upper  part  of  the  condenser, 
whence  it  falls  through  the  strainer,  CC',  and  meets  and  con- 
denses steam  which  enters  from  the  cylinder  through  the  nozzle 
DjD'jD".  A  few,  only,  of  the  numerous  holes  in  the  strainer 
are  shown  in  the  plan. 

E'E"  is  a  manhole,  covered  by  a  plate,  for  affording  access  to 
the  interior  of  the  condenser.  FjF'jF"  is  a  slanting  flange  by 
which  the  condenser  is  kept  in  place  relatively  to  the  gallows 
frame  which  supports  the  working  beam.  The  lugs,  bb,  and 
the  lower  brackets  fi,H',H",  afford  bearings  for  bolts  which 
fasten  the  condenser  to  the  bed-plate,  PL  YIIL,  and  parts  ad- 
jacent. The  upper  brackets,  G,G',G",  give  bearing  for  tie 
rods  which  bind  the  beam-pillow  block  and  the  condenser  to 
a  fixed  relative  position.  The  strainer  rests  on  lugs,  as  aa '. 
The  lower  surface  1S"'N'  of  the  condenser,  rests  on  the  bed-plate, 
and  its  top  rim  c'd' — c"d"  is  the  bearing  for  the  cylinder. 

Construction. — The  small  scale  of  ^  inch  to  1  foot  may  well 
be  enlarged  to  not  more  than  1  inch  to  1  foot.  The  curve 
KL — K'L' — K"L"  is  the  elliptical  intersection  of  the  oblique 
front  plane  of  the  flange,  F,F',F",  with  the  vertical  cylindrical 
outside  of  the  condenser.  It  is  readily  constructed  by  points, 
by  simply  considering  that  any  ordinate,  as  A/7,  upon  the  centre 
line  Mrz-  of  the  plan,  will  be  vertically  projected  at  F',  and  on 
Fig.  3  at  h"f"=hf,  and  laid  off  from  the  centre  line  n"u". 


38  ELEMENTS   OF 

EXAMPLE  XII. 

A  Surface  Condenser. 

Description. — Any  surface  condenser  is  an  arrangement  of 
parts  such  as  to  bring  confined  steam  into  contact  with  a  large 
area  of  surface  which  is  kept  cold.  PI.  V.,  Figs.  4,  5,  6,  7,  and 
8,  gives  sufficient,  though  not  entirely  complete,  views  of  a  sur- 
face condenser,  as  built  by  the  Novelty  works  at  New  York 
for  the  recent  Pacific  Mail  steamers. 

In  this  condenser  are  4.224:  tubes  of  galvanized  brass,  each 
about  9  feet  long,  £  inch  outside  and  -^  inside  diameter,  in- 
serted at  the  ends  in  tube  plates,  I.,  Fig.  7,  where  a  tight  joint 
is  made  by  a  collar  or  packing  of  compressed  wood,  gp,  around 
the  tube. 

A,A"  is  the  bed-plate,  see  PL  VIIL,  through  a  passage  in 
which,  water  is  forced,  entering  the  condenser  at  L,  and  passing 
through  the  tubes  and  out  through  the  out-board  delivery,  O, 
as  indicated  by  the  arrows  W,W,W,  Fig.  5.  B,BBB  is  the  con- 
denser proper,  into  which  steam  enters  from  the  cylinder,  C, 
through  the  exhaust  valve  at  ee,  and  as  shown  by  the  arrows 
s,s,s.  It  is  condensed  by  contact  with  the  cold  tubes ;  and  as 
it  is  not  mixed  with  the  cold  water  of  the  tubes,  it  forms  fresh 
hot  water  for  the  supply  of  the  boilers.  This  water  flows  into 
the  lower  part  of  the  bed-plate  A,  whence  it  is  lifted  by  the  air- 
pump,  P,  into  the  hot  well,  and  thence  pumped  into  the  boiler. 

The  covers,  FF,  Fig.  6,  of  the  separate  openings  in  the  skele- 
ton frame  of  the  condenser,  are  called  bonnets.  F',  at  the  left, 
is  an  edge  view  of  one  of  them.  At  HH,  one  of  the  bonnets  is 
removed,  showing  some  of  the  tubes.  D  is  the  rounded  con- 
denser cover.  KK",  not  shown  in  the  plan,  Fig.  4,  is  the  flange 
resting  against  the  gallows  frame  GG.  Fig.  8  is  its  horizontal 
projection,  corresponding  in  position  with  K.  S",SS  is  the 
steam-chest ;  N,  the  steam-pipe  nozzle ;  Q  and  Q',  the  steam 
and  exhaust  pipe. 

Fig.  7  is  a  detail,  enlarged,  of  an  edge  view  of  part  of  a  tube 
plate,  showing  the  wood  packing^?. 

Construction. — The  scale,  except  in  Fig.  7,  is  very  small.  A 
scale  of  from  |-  to  y^-  would  be  much  better. 


MACHINE   CONSTRUCTION   AND   DRAWING.  39 

SECTION  II.— GENERAL  SUPPORTERS. 
A— Point  Supporters. 
B— Line  Supporters. 

Standards. 

53.  STANDARDS,  otherwise  called,  without  much  distinction, 
posts  or  columns,  are  those  upright  supporters  around  which 
the  working  parts  are  mostly  arranged.  It  may  be  said  that 
standards  and  posts  are  fastened  only  at  bottom,  but  columns 
at  both  ends. 

This  class  of  supporters  is  found  in  connection  with  upright 
drilling  machines,  power  hammers,  etc. 

The  two  following  examples  are  chosen  for  their  excellence 
in  affording  practice  in  drawing  compound  curves,  and,  in  part, 
the  intersections  of  surfaces. 

EXAMPLE  XIII. 
The  Standard  of  a  Power  Hammer. 

Description. — This  example,  PI.  YL,  Fig.  1,  represents  the 
standard  for  one  of  Shaw  and  Justice's  patent  dead-stroke 
power  hammers,  with  a  100  Ib.  hammer.  It  presents  some 
points  of  such  novelty  and  interest  and  value,  as  indicated 
by  extensive  use,  that  the  following  general  description  precedes 
that  of  the  standard  separately. 

Fig.  16  gives  a  general  view  of  the  whole  machine,  in  two 
elevations. 

A  is  the  hammer,  working  vertically  in  guides  B.  It  is 
attached  by  the  belt  and  links,  CO,  to  the  heavy  bow  spring, 
DD,  which  in  turn  is  actuated  by  the  connecting  rod,  E,  from  a 
crank  pin  on  the  wheel  J. 

A  band  wheel,  L,  on  the  same  axis,  actuates  the  whole 
machine.  Its  band,  however,  is  loose,  and  is  made  to  act  by 
pressing  down  the  treadle,  IIII,  which  draws  up  the  "idler 
wheel,"  GG,  against  the  band  (not  shown),  and  makes  it  bind. 

The  same  operation  also  slacks  the  leather  brake,  MM, 
and  leaves  the  machine  free  to  act.  "When  the  treadle  is  let  go, 


40 


ELEMENTS    OF 


the  land  is  slacked  and  the  brake  tightened,  by  the  falling 
back  of  G,  and  the  hammer  is  instantly  stopped. 


To  understand  the  action  of  the  spring,  it  must  be  understood 
that  the  hammer  acts  with  great  velocity,  making,  for  a  100  Ib. 
hammer,  about  250  strokes  per  minute.  At  the  instant,  then, 
that  the  spring  begins  to  ascend,  the  resistance  of  the  hammer 
compresses  it  somewhat,  and  when  it  begins  to  descend,  the 
momentum  of  the  hammer  carries  it  upward,  still,  a  short 
distance,  which  causes  a  strong  compression  of  the  spring, 
while  the  belt  CO  will  be  slightly  curved  upwards.  Then,  in 
the  remainder  of  the  descent,  the  recoil  of  the  spring  acts  with 
great  force  to  straighten  the  belt  and  draw  down  the  hammer 
much  more  powerfully  than  its  mere  free  descent,  through  so 
short  a  space,  could  do.  The  spring  further  acts  to  pick  up  the 


MACHINE   CONSTRUCTION   AND   DRAWING.  41 

hammer  instantly  after  its  blow  has  been  given,  so  that  the 
foundations  are  less  beaten  than  by  a  drop  hammer. 

The  connecting  rod  is  in  several  pieces,  coupled  with  right 
and  left  screws,  so  that  its  length  can  be  adjusted  by  turning  its 
parts  by  pins  inserted  in  its  holes,  so  as  to  give  any  desired 
distance  between  the  hammer  and  the  anvil. 

Construction. — This  is  shown  in  PL  VI.,  Fig.  1,  by  two 
elevations  and  a  horizontal  section  through  the  guides.  The 
scale  used  was  that  of  half  an  inch  to  the  foot.  A  scale  of 
double  that  size,  as  shown  in  the  section,  is  recommended. 

As  any  two  projections  of  an  object  often  reveal  all  its 
dimensions  with  sufficient  clearness,  the  student  can  often 
exercise  himself  to  great  advantage  by  constructing  other  views 
than  the  ones  shown,  from  the  measurements  given.  Thus,  in  the 
present  case,  a  plan  could  be  constructed,  and  a  vertical  section. 

"With  the  full  measurements  given  in  this  example,  no  further 
directions  for  its  construction  seem  necessary. 

Execution. — Under  this  head  but  few  remarks  have  hitherto 
been  made,  as  the  plates  have  been  supposed  to  be  executed 
simply  in  lines.  Some  of  the  figures,  and  this  one  among 
others,  might  be  fully  shaded  with  excellent  effect;  in  this 
case,  on  account  of  the  numerous  bluntly  rounded  edges. 
"When  thus  shaded,  a  figure  need  have  no  ink  lines  at  all  upon 
it,  all  the  sharp  edges,  if  there  be  any,  being  well  shown  by  the 
contrast  of  shades  between  the  adjoining  surfaces,  or  by  leav- 
ing a  narrow  line  of  lighter  shade  on  edges  exposed  to  the 
light,  and  of  darker  tint  on  edges  which  are  lines  of  shade. 

54:.  Having  in  view  the  advantage  of  comparing  different 
means  of  attaining  the  same  object,  the  following  figures  and 
description  of  a  very  elegant  species  of  spring  power  hammer 
are  added.  The  description  is  nearly  in  the  words  of  the  manu- 
facturer's circular.  The  machine  is  known  as  Hotchkiss's 
patent  Forge  Hammer. 

Description. — The  Hammer  represented  by  Figs.  17  and  18 
claims 

1st.  Simplicity  and  Durability. 

2d.  Economy  of  Power  and  Space. 

3d.  Striking  square  with  a  sharp  and  elastic  blow. 

It  runs  with  little  noise,  and  by  the  peculiar  arrangement 
of  the  cylinder  and  piston,  the  hammer  is  driven  by  air-springs, 


ELEMENTS    OF 


which  saves  the  machine  from  jar,  other  than  the  blow  on  the 
anvil  or  work ;  and  can  be  used  in  any  building  without  in- 
juring the  foundation  or  walls. 

The  cylinder  and  hammer 
moving  in  vertical  slides,  each 
blow  is  square,  exactly  in  the  same 
place,  and  some  kinds  of  die  work 
can  be  forged  as  exact  as  under 
a  drop,  with  greater  rapidity.  It 
is  under  the  perfect  control  of 
the  operator,  can  strike  light  or 


I 


heavy,   slow    or    fast,    as   desired,   and   will   draw,   weld,   or 
swage. 

The  hammer  derives  the  increased  force  of  its  blow  from 
the  reaction  of  compressed  air  upon  the  piston.  The  air 
is  compressed  within  the  cylinder  A  by  the  piston  B 
which  fits  the  cylinder,  air-tight.  (See  Fig.  18.)  The 
cylinder  moves  in  the  slides  C  by  the  action  of  the  con- 
necting-rod D,  driven  by  the  wrist  pin  in  the  face  plate 
E  by  belting,  in  the  usual  manner.  The  cylinder  is  air- 
tight at  each  end  ;  there  are  two  small  holes  F  in  the  cylinder. 


MACHINE   CONSTRUCTION   AND   DRAWING.  43 

through  which  the  air  passes  freely  in  and  out,  which  supplies 
any  leakage,  and  prevents  a  vacuum  behind  the  piston  as  it 
passes  beyond  the  air-ports  either  way. 

The  piston,  piston-rod,  and  hammer  are  entirely  independent 
of  the  cylinder,  and  can  be  moved  up  and  down  without  moving 
the  cylinder /  when  the  cylinder-is  moved  either  way,  the  piston 
passes  the  air-ports  F,  confining  the  air  in  either  end  of  the 
cylinder,  which  prevents  the  heads  striking  the  piston,  and  acts 
as  a  spring,  lifting  the  hammer  up  or  accelerating  its  downward 
movement.  The  cylinder  has  a  definite  motion,  governed  by  the 
travel  of  the  crank,  but  the  hammer  has  more  lift,  according  to 
the  compression  of  the  air. 

If  the  cylinder  is  moved  up  and  down  slowly,  there  is  no  blow 
given,  as  the  weight  of  the  hammer  hangs  on  the  cushion  of 
air,  under  the  piston,  in  the  bottom-  of  the  cylinder.  If  the  cyl- 
inder is  moved  up  quickly,  the  air  under  the  piston  lifts  the  pis- 
ton and  hammer  as  quickly  to  the  highest  point  the  crank  will 
allow  the  cylinder  to  go ;  then,  the  momentum  the  hammer  has 
acquired,  causes  the  hammer  to  go  higher,  which  pushes  the 
piston  up  in  the  cylinder  and  compresses  the  air  in  the  upper 
portion,  which  acts  as  a  spring  to  accelerate  the  downward  mo- 
tion of  the  hammer. 

In  addition  to  the  weight  of  the  hammer,  and  the  reaction  of 
the  upper  air  spring  upon  the  piston,  the  upper  head  of  the  cyl- 
inder as  it  comes  down  drives  the  piston  and  hammer  down  with 
the  same  rapidity  with  which  it  was  raised ;  thus,  by  a  rapid 
reciprocating  motion  of  the  cylinder,  quick  and  sharp  blows 
are  given. 

The  blow  is  according  to  the  speed  at  which  the  hammer  is 
run,  for  when  running  at  high  speed  the  upper  air  spring  is  more 


The  speed  is  regulated  by  the  idler  pulley  operated  by  the 
treadle.  But  if  it  is  wished  to  run  rapidly  and  lightly,  raise  the 
cylinder  by  lengthening  the  rod  by  the  double  nut  on  it,  which 
allows  the  lower  air-cushion  to  take  the  bulk  of  the  blow.  The 
hammer,  after  being  driven  down,  is  instantly  picked  up  by  the 
ascending  air-cushion,  without  any  shock  or  jar;  and  so  long  as 
the  packings  are  tight,  it  can  be  run  for  years  with  little  wear. 
These  packings  are  as  simple  as  a  pump-packing,  durable  and 
easily  renewed. 


44  ELEMENTS   OF 

C— SURFACE  SUPPORTERS, 
a — Plane  Supporters. 
Frames. 

55.  FRAMES  are  those  general  supporting  members  of  ma- 
chines which,  according  to  the  usual  meaning  of  the  term,  en- 
close certain  open  areas,  one  or  more.  They  are  also  the  more 
immediate  supports  of  moving  pieces,  whose  centres  or  paths 
of  motion  they  hold  in  fixed  relative  positions. 

So  various  are  the  forms  and  uses  of  machines,  and  so  depen- 
dent is  the  form  of  the  frame,  in  each  separate  case,  upon  the 
intended  use  of  the  machine,  that  it  may  not  be  possible  to  pre- 
sent a  complete  or  well-defined  classification  of  frames. 

Still,  the  mind  may  be  guided,  in  ranging  through  multiplied 
examples  of  frames,  by  the  following  view  of  the  more  conspi- 
cuous varieties  of  familiar  or  novel  designs. 

FRAMES,  then,  are 

Beam  frames;  as  in  the  general  frames  of  locomotives,  car 
trucks,  etc. 

Webbed  ;  when  thin,  and  embracing  many  regular  and  irreg- 
ular openings.  "Webbed  frames  appear  in  the  two  principal 
forms  of  plane,  as  in  the  end  frames  of  spinning  machines ; 
and  closed,  as  in  case  of  some  upright  engines,  whose  vertical 
prismatic,  or  more  commonly  pyramidal  frames,  consist  of 
perforated  plates  joined  at  the  cornel's  to  form  a  frustum  of  a 
hollow  pyramid,  upon  and  within  which  the  working  parts  are 
supported. 

Trunk  frames  ;  as  that  of  a  Corliss'  upright  engine,  which 
is  a  frustum  of  a  cone  with  a  circular  or  oval  base,  as  may  be 
most  convenient,  and  whose  convex  surface  is  continuous,  except 
as  broken  by  one  or  more  large  openings,  to  allow  access  to 
the  interior. 

Jointed;  as  those  of  many  beam  engines,  and  vertical  direct- 
acting  engines.  The  columns  found  in  such  frames  are  some- 
times inclined,  forming  an  open  pyramidal  frame.  Jointed 
frames  are  also  sometimes  composed  in  part  of  rods  united  by 
joints,  as  in  the  frame  of  Wheeler's  "tumbling  beam"  engine,  etc. 

Consolidated;  where,  for  the  greatest  rigidity,  and  security 
from  displacement  by  shocks,  the  local  and  general  supporters, 


MACHINE   CONSTRUCTION   AND   DRAWING.  45 

and  other  fixed  parts,  are,  as  far  as  possible,  consolidated  into 
one  piece,  as  in  Reynolds'  three-cylinder  engine  for  reversing 
at  full  speed  under  full  steam.  The  same  idea  is  also  illustra- 
ted in  those  steam  hammers  in  which  the  steam  cylinder  and 
frame  are  one  piece,  and  in  the  Corliss,  and  the  Babcock  and 
Wilcox  horizontal  engines. 

In  the  study  of  frames,  the  principal  things  to  be  sought 
are,  first,  the  combination  of  lightness  with  strength ;  second, 
easy  access  to  all  the  attached  working  parts ;  third,  whatever 
grace  of  outline  can  be  had ;  fourth,  and  as  a  means  thereto, 
the  solution  of  the  numerous  problems  of  tangent  curved  and 
straight  lines  which  occur  in  designing  open  frames. 

In  illustrating  a  few  specimens  only  of  the  above  descriptive 
list  of  frames,  which  is  all  that  seems  to  be  necessary,  we  have 
taken  examples  differing  from  each  other  as  much  as  possible, 
and  presenting,  otherwise,  useful  exercises  for  practice. 


EXAMPLE  XIY. 

Locomotive  Frames. 

General  Principles. — In  the  construction  of  the  modern 
American  locomotive,  the  objects  sought  are  unity  and  firmness 
in  the  assemblage  of  principal  parts,  and  ready  self -adjust- 
ment, with  durability,  in  the  running  parts. 

To  secure  the  first  object,  the  boiler,  with  its  enclosed  fire- 
box; the  frame,  and  the  heavy  castings  which  embrace  the 
cylinders,  are  all  strongly  united  so  as  to  act  substantially  as  one 
piece. 

To  secure  the  requisite  flexibility,  with  steadiness,  the  springs 
over  the  two  driving  axles  are  linked  to  a  balance  beam,  the 
flange  on  the  forward  driving  wheel  is  omitted,  and  the  front 
end  of  the  engine  is  supported  at  points  on  the  transverse  centre 
line  of  the  truck,  whose  wheels  are  far  apart,  so  that  a  slight 
vertical  displacement  of  any  of  them  occasions  but  a  slight 
movement  of  the  central  points  of  support. 

The  frames  are  of  wrought  iron,  in  a  few  heavy  f orgings,  and 
are  next  to  the  inner  sides  of  the  driving  wheels. 

The  figures  2,  3,  and  4:  on  PI.  VI.  show  two  different  styles 
of  frame. 


46  ELEMENTS    OF 

Description. — PL  YL,  Fig.  2,  shows  the  essential  parts  of  the 
frame  of  locomotive  21,  on  the  Boston,  Hartford,  and  Erie  R. 
R. ;  now  (1868)  nearly  new. 

GG — G'G'  is  the  main  portion,  and  is  solid  with  the  jaws, 
EE,  which  embrace  the  axles,  K,  and  the  axle  boxes  not  shown. 

The  portion  at  cd  is  reduced  to  the  thickness  shown  at  e  in 
the  plan.  HH — H'H',  the  forward  section  of  the  frame,  is 
fastened  to  the  rear  section  GG'  at  e — cd  and  to  the  forward 
jaw  E  by  bolts,  as  shown.  The  stirrups,  FF,  are  bolted  to  the 
frame  by  four  bolts  each.  The  lugs,  LL,  mark  the  points  of  at- 
tachment of  the  cylinder  to  the  frame. 

The  plain  portions  of  the  frame  are  broken  out,  that  the  more 
important  parts  may  be  shown  on  a  larger  scale. 

Figs.  3  and  4  show  a  slightly  different  style  of  frame,  and 
also  one  of  the  adjusting  wedges,  not  shown  in  Fig.  2,  showing 
the  manner  of  setting  the  axle  boxes,  so  as  to  secure  the  correct 
distance  between  the  axles  of  the  two  driving  wheels,  on  the 
same  side  of  the  engine. 

In  this  frame,  the  stirrups  are  all  alike,  with  horizontal  bear- 
ings, and  each  is  held  by  two  bolts. 

The  inner  sides,  as  ac,  of  the  jaws,  converge  upwards,  as  seen 
in  both  frames. 

One  of  the  adjusting  wedges  is  separately  shown  in  Fig.  4. 
Its  flanges  ha — h'a',  and  jyq,  clasp  the  jaw  E,  its  interior  width 
being  seen  to  be  the  same  as  the  thickness  of  the  frame.  The 
surface  ac  bears  against  the  jaw,  and  the  vertical  surface,  ed, 
against  the  axle  box.  By  the  nuts,  N,N',  the  wedge  is  raised  and 
lowered.  When  raised  its  ascent  along  the  taper  of  the  jaw 
crowds  the  axle  box  to  the  right,  or  forward.  D  is  a  clamp 
screw,  which  holds  the  wedge  tight  against  the  box.  A  similar 
one,  bearing  against  the  opposite  wedge,  not  shown,  each  acts  as 
a  check  nut  to  the  other. 

The  action  of  a  check  or  jam  nut  is  thus  explained :  When  a 
single  nut,  as  1ST,  is  screwed  up  to  its  bearing,  any  jar  which 
turns  it  free  from  the  bearing  leaves  it  loose  on  the  screw,  and 
liable  to  work  off.  But  when  a  second  nut,  N',  on  the  same 
screw  is  brought  home,  each  clamps  the  other  to  the  threads  of 
the  screw,  as  well  as  to  the  bearing,  so  that  neither  is  so  apt  to 
get  loose. 

The  nuts  may  bear  directly  against  each  other  as  well  as  on 
opposite  sides  of  an  intervening  piece  S,  as  in  Fig.  3. 


MACIIINE    CONSTRUCTION    AND   DRAWING.  47 

The  bolt  heads  in  the  main  joint  MM7  are  countersunk,  that 
is,  let  into  the  iron,  nearly  their  whole  depth. 

In  the  West  Albany  Machine  Shops  of  the  1ST.  Y.  Central 
R.  R.,  where  the  data  for  Fig.  3  and  several  other  examples 
were  obtained,  locomotive  building,  as  well  as  repair,  is  carried 
on  to  such  an  extent  that  an  admirable  uniformity  of  like  parts 
in  all  engines  of  the  same  class  now  built  there,  has  been  secured 
by  means  of  a  system  of.  steel  gauges  for  internal  and  external 
turned  work,  and  of  nuts  and  bo'lts  for  all  pai'ts  of  an  engine. 

Construction. — From  the  full  measurements  given,  either  or 
both  of  these  frames  can  now  be  drawn  without  further  ex- 
planation ;  simply  observing  that  always,  where  a  large  number 
of  equal  bolts  are  used,  it  is  sufficient  to  show  one  or  two  of 
them  and  indicate  the  positions  of  the  rest  by  their  centre  lines, 
as  shown  in  figures  2  and  3.  - 

PL  TIL,  Fig.  6,  gives  a  sketch,  merely,  with  measurements  of 
a  web-frame  for  the  support  of  a  lathe  bed.  It  affords  very  good 
practice  in  compound  curves,  suitable  centres  for  which  can  be 
adjusted  to  the  given  measurements,  by  the  student. 


"b — Developable   Supporters. 

Beds. 

56.  Bed  plates,  or,  simply,  beds,  are  the  general  supporters  of 
engines  and  other  heavy  machines,  consisting  of  several  parts 
resting  on  a  common  foundation. 

They  are  usually  of  cast  iron  and  made  in  one  piece,  or  in 
sections,  firmly  bolted  together,  according  to  their  size.  They 
rest  immediately  upon  the  masonry  foundation  beneath  them ; 
and,  being  in  one  piece,  accord  with  the  important  structural 
principle  of  continuous  bearings,  for  what  they  serve  to  sup- 
port. 

Bed  plates  may  be  described,  as  to  their  varieties,  as  flat  bed 
plates,  when  consisting  simply  of  a  flat  plate  on  which  the  sup- 
porting frame-work  of  an  engine  rests ;  box  bed  plates ;  open, 
when  consisting  of  four  sides  in  one  piece  surrounding  an  in- 
terior space,  open  at  top  and  bottom,  as  seen  in  many  horizontal 
engines.  These  bed  plates  are,  moreover,  usually  symmetrically 


48  ELEMENTS   OF 

divided  by  a  vertical  plane  through  the  axis  of  the  cylinder. 
See  Fig.  19. 


There  are  also  covered  box  beds,  that  is  like  the  last,  only  closed 
on  top,  narrow,  and  having  the  guide,  cylinder,  etc.,  bolted  to 
them  on  one  side ;  as  in  N.  T.  Green's  horizontal  engines ;  and 
tank  beds,  which  are  hollow  and  answer  for  other  purposes  than 
that  of  mere  support.  Among  these  we  distinguish,  marine  en- 
gine tank  or  hollow  bed  plates — see  PI.  VIII. — and  pier  tank  beds 
which  are  quite  massive,  and  proportioned  with  such  breadth  of 
base  as  to  preclude  the  necessity  in  many  cases  of  a  separate 
masonry  foundation.  These  are  used  more  for  portable  hori- 
zontal engines,  though  a  very  common  practice  is  to  make  the 
boiler  strong  enough  to  serve  also  as  a  bed  for  such  engines. 


EXAMPLE  XY. 

A  Prismatic  Beam-led  and  Pedestal. 

Description. — PI.  VII.,  Figs.  1-5.  This  beam-bed  is  from  a 
Babcock  &  Wilcox  horizontal  engine  of  10"  bore  and  30"  stroke 
of  piston.  It  is  shown  in  elevation,  and  three  vertical  sections, 
at  AB,  CD,  and  EF.  The  two  sections  at  CD  and  EF  are 
taken  looking  towards  the  cylinder,  and  show  all  in  and  beyond 
their  planes. 

By  pointing  out  the  different  projections  of  numerous  points, 
and  by  comparison  of  measurements,  and  distances  with  the 
dividers,  the  student  will  be  able  to  appreflend  the  form  of  this 
somewhat  irregular,  but  very  neat  and  substantial  frame  or  bed. 
The  entire  frame,  or  engine  support,  embraces  the  standard 
pillow-block  or  pedestal,  MP,  the  bed-piece,  HH,  and  the 
cylinder  with  its  pedestal,  not  shown,  which  are  all  bolted 
together,  as  at  gg  and  ram,  so  as  to  act  as  one  piece. 


MACHINE   CONSTKUCTION   AND   DKAWING.  49 

In  the  bed-piece,  on  all  the  figures,  L  is  its  vertical  web,  KK 
its  ribbed  lateral  wings,  on  the  back,  and  GG  those  on  the 
front,  which  are  shaped  to  act  as  guides.  I,R,  is  the  back 
Cylinder  head,  and  the  parts  within  IHH',  form  the  stuffing- 
box.  The  inner  circle,  <?,c,£,  is  that  around  the  piston-rod,  and 
d,  e,  and /are  circles  of  the  cylinder-head,  as  seen  by  comparing 
Figs.  1,  4,  and  5.  m,m,m,w,  are  some  of  the  bolt-holes  through 
which  the  bed  is  bolted  to  the  cylinder-shell.  Q  is  the  back 
end  of  the  steam-chest,  and  h  the  collar  around  the  valve-stem. 
The  hollow  square  guide  k  and  parts  adjacent,  Fig.  4,  are  for 
the  support  of  some  of  the  moving  parts.  The  disappearance 
of  edges  into  a  plane  surface  is  shown,  as  at  r,r. 

The  ribs,  K,K,  are  partly  shown,  dotted,  in  Fig.  1.  The  long 
curves  of  the  bed  and  pillow-block  are  constructed  by  ordinates ; 
and  in  part  by  circular  arcs,  as  shown. 

The  pillow-block,  MP,  Figs.  1  and  2,  may,  as  said  before  in 
Ex.  III.,  be  drawn  separately ;  and  on  a  scale  of  one-sixth,  one- 
fifth,  or  one-fourth.  It  is  largely  hollow,  as  indicated  by  the 
dotted  lines,  next  to  the  outer  ones,  ss  is  the  diameter  of  the 
shaft.  Only  the  larger  measurements  are  given.  The  rest  can 
be  found  from  the  scale.  The  boxes  are  adjustable  laterally,  as 
is  proper  in  all  blocks  for  horizontal  engines,  by  set-screws  and 
jamb-nut,  as  atj?,  q.  IS"  and  O  are  moulded  edges. 

A  plan  may  be  substituted  for  Fig.  2,  or  a  vertical  cross 
section  through  its  centre. 

Figs.  1  and  2  should  stand  on  the  same  line,  so  as  to  favor  the 
projecting  of  points  from  one  to  the  other. 

Construction. — As  in  all  such  cases,  lay  out  the  longer  and 
outer  lines  first,  and  fill  in  the  smaller  parts  afterwards.  The 
proper  heavy  lines  are  nearly,  if  not  all,  indicated  by  two  dashes 
across  them. 


D— VOLUME  SUPPORTERS. 

EXAMPLE  XVI. 
A  Tank  Bed-plate. 

Description. — This  example,  PI.  VIII.,  is  an  excellent  one, 
representing  the  bed-plate  for  a  beam-engine,  as  built  by  the 
Novelty  Iron  Works  of  New  York  for  the  Pacific  Mail  Steam- 
4 


50  ELEMENTS    OF 

ship  Co.'s  steamers,  of  the  class  having  cylinders  of  105"  di- 
ameter and  12  stroke  of  piston. 

Fig.  1  is  a  plan  of  the  bed-plate.  Fig.  2  shows  a  longitudi- 
nal section  made  by  the  vertical  plane  MX.  Fig.  3  shows  a 
transverse  section  made  by  the  vertical  plane  PQ.  Fig.  4  is  a 
fragment  of  an  elevation,  as  seen  in  looking  into  the  opening  at 
BB'. 

Over  the  chamber  EE',  on  the  surface  CCC— C'C'— C"C"- 
C"' — see  the  several  figures — the  condenser,  square  in  plan  and 
fastened  by  bolts  through  JJ,  etc.,  is  set.  Over  the  condenser 
is  the  steam  cylinder,  which  is  vertical.  The  condenser  here 
supposed  is  of  the  kind  called  surface-condensers,  Ex.  XII.,  con- 
sisting of  a  tight  central  chamber  over  E<2,  through  which  many 
tubes  pass,  from  a  side-chamber  over  DD — d',  to  an  opposite 
side-chamber  over  11,1'.  Water  is  delivered  to  the  condenser 
from,  a  steam-pump,  through  the  passages  DD — D'D' — D"D", 
which  begin  at  BB" — B' — B'".  These  passages  lead  over  the 
arch,  ff,  Fig.  3,  which  is  at  DD  in  the  bed-plate,  and  the  water 
enters,  through  DD — d',  the  side-chamber  over  that  opening. 

Exhaust-steam  from  the  cylinder,  entering  the  condenser,  is 
liquefied  by  contact  with  the  multitude  of  cold  tubes  which  tra- 
verse its  central  chamber,  and  the  water  of  condensation  flows 
to  the  right-hand  part,  KK',  of  the  hollow  bed,  where  it  is 
removed  by  the  air-pump,  which  also  maintains  the  vacuum  in 
the  condenser. 

The  air-pump  stands  at  A  A — A 'A' — A."  A." — A'".  "Valves 
at  FF — F',  called  the  foot  valves,  prevent  the  re-flow  of  air  and 
water  to  the  condenser,  when  the  air-pump  bucket  or  piston 
descends.  FF — C'G'  are  openings  to  give  access  to  the  foot- 
valves,  and  are  covered  by  a  bonnet.  H  is  the  opening  for 
a  pipe  leading  from  the  bilge  to  the  condenser,  and  used  in  case 
the  vessel  springs  aleak.  The  vacuum  in  the  condenser  causes 
water  to  flow  into  it  from  the  bilge,  which  is  then  removed 
by  the  air-pump,  mm'  is  a  manhole  for  entrance  to  the  bed- 
plate. 

The  surfaces  to  which  the  word  "  faced "  is  attached  are 
planed,  to  secure  accurate  bearings  and  tight  joints. 

Construction. — The  plan  being  entirely  symmetrical,  except 
the  difference  between  the  holes,  mm'  and  H,  it  would  be 
sufficient  to  draw  just  enough  more  than  half  of  it  to  include 
both  of  those  openings. 


MACHINE   CONSTRUCTION   AND   DRAWING.  51 

The  completeness  of  the  measurements,  and  the  repetition  of 
many  of  them,  will  aid  in  understanding  the  foregoing  de- 
scription ;  and  as  no  directions,  besides  those  already  given  in 
previous  problems,  are  necessary,  the  drawing  is  here  left  to  the 
student,  with  the  correct  location  of  the  heavy  lines  on  Figs. 
1  and  2,  as  a  study.  These  lines  can  generally  be  found  by 
inspection,  by  careful  attention  to  the  principles  of  (47). 


EXAMPLE  XVII. 

Housing  or    Chambered   Frame  for    a   Reversible    Rolling 
Mill  Engine. 

Description.— Pis.  IX.,  X.,  and  XL  [Let  Plate  X.  be  cut 
out  and  pasted  at  the  top  edge  to  Plate  IX.,  so  that  their  centre 
lines  AB  and  AB  shall  coincide  in  direction,  fhen  paste 
Plate  XL  to  the  right  hand  of  Plates  IX.  and  X.,  so  that  the 
lines  CD  shall  be  in  the  same  horizontal  direction.  The  three 
projections  will  thus,  if  it  be  desired,  be  brought  into  proper 
relative  position  for  reference.]  This  remarkable  design  is 
from  an  engine  designed  by  Gr.  H.  Reynolds,  of  New  York, 
in  1866,  for  a  steel  rolling  mill  at  Troy,  K  Y. 

A  very  similar  arrangement  is  described*  as  an  English 
invention  patented  by  a  Mr.  M'Naught,  viz.,  three  radially 
equidistant  cylinders,  fixed  in  a  common  frame,  with  the 
connecting  rods  jointed  to  a  common  crank  pin,  and  the  valves 
worked  by  one  eccentric. 

The  rolls  of  a  rolling  mill  usually  consist,  as  described  in 
the  next  example,  of  three  lines 
of  horizontal  cylinders,  one  above 
another,  and  with  circular 
grooves  around  them,  shaped  to 
the  section  of  the  bar  to  be 
rolled.  If,  then,  a  piece  shoot 
through  between  the  upper  rolls 

A ^-^ s      as  shown  at  «,  Fig.  20,  one  rolled 

Fl°-  so- through  the  lower  rolls  will  re- 
turn as  at  J,  from  the  workman  at  B,  to  the  one  at  A.  This  is  re- 

*  Imp.  Cyc.  Machinery. 


52  ELEMENTS    OF 

peated,  through  the  different  approximately  shaped  pairs  of 
grooves  which  lie  together  along  the  same  rolls,  until  the  final 
form  is  given  to  the  manufactured  bar. 

To  accomplish  this  alternate  passage  of  the  bar  with  only 
two  rolls,  their  motion  must  be  reversed  every  time  the  bar 
passes  them. 

The  rolls  revolve  very  rapidly;  they  require  an  immense 
power  to  actuate  them  when  numerous ;  and  to  save  time,  loss 
of  which  would  fatally  cool  the  bar,  they  must  be  reversed 
instantly.  To  fulfil  these  cardinal  conditions  by  direct  action, 
that  is,  without  gaining  the  necessary  speed  by  gearing  from  the 
engine  shaft,  is  the  object  of  the  novel  engine  here  partly 
illustrated. 

This  engine  was  to  be  of  3,000  horse  power,  to  make  some 
300  revolutions  per  minute,  and  to  be  instantly  reversible  at 
that  speed,  with  steam  on,  many  times  per  minute.  One  of  the 
lines  of  rolls  was  to  be  on  the  same  shaft,  S,  PL  XI.,  with 
the  engines,  and  would  be  geared  to  the  other. 

To  secure  this  high  shaft-velocity,  without  excessive  piston 
speed,  the  cylinders,  of  which  there  were  to  be  three,  placed 
120°  apart,  as  shown  on  Pis.  IX.  and  X.,  were  to  be  of  three 
feet  diameter,  and  only  one  foot  stroke.  To  secure  the  great 
po^oer  required  for  many  rolls,  without  cylinders  too  large  for 
the  required  velocity,  there  were  to  be,  as  stated,  three  cylinders, 
of  which  one  was  to  be  vertical.  This  arrangement,  also,  would 
apply  the  power  more  equally  to  the  shaft,  and  with  never  but 
one  "  dead  point "  at  a  time.  Finally,  to  provide  against  the 
great  strain,  and  dislocation  of  parts,  arising  from  the  many 
quick  reversals,  the  three  cylinders  and  the  frame,  enclosing 
all  the  steam  passages,  were  to  be  in  one  huge  casting. 

PI.  IX.,  Fig.  1,  shows  the  plan  of  the  engine,  with  a  partial 
section  of  the  vertical  steam-chest,  OO,  and  slide-valve,  DD. 
Here  EEE  is  the  branching  steam-pipe,  and  F,F,F  are  the  verti- 
cal central  planes  of  the  three  cylinders,  placed  far  enough 
apart,  laterally,  to  allow  their  respective  connecting  rods  to  act 
side  by  side  on  the  same  long  crank  pin,  P,  PI.  XI.  QA  is  the 
top  cover  of  the  vertical  cylinder.  L,  O,  and  L'  are  the  three 
steam-chests,  and  the  oblique  cylinders  are  shown  in  dotted 
lines.  Steam  enters  through  the  pipe,  E,E,  and  distributes 
itself,  as  shown  by  the  arrows,  through  the  general  steam-pas- 
sage, T,  to  the  three  cylinders.  Escaping  through  whichever 


MACHINE    CONSTRUCTION   AND   DKAWING.  53 

steam -port  is  at  the  moment  under  the  valve,  it  flows,  as  at  D, 
into  the  exhaust  passage,  Iv.  The  cylinders  are  thus  steam- 
jacketed,  both  by  the  live  and  exhaust  steam. 

PL  X.  shows  the  front  elevation.  CD  is  the  sole  of  the 
frame,  which  is  of  cast-iron,  whole.  Its  upper  part,  FG-B,  is 
not  exactly  of  uniform  radial  width,  its  three  outer*semicircles 
being  described  from  a  centre,  O',  2  ins.  below  the  principal 
centre,  O.  The  three  cylinders  are  shown  in  dotted  lines,  with 
their  steam  and  exhaust  ports.  E  and  E,  at  the  upper  cylinder, 
are  sections  of  the  steam  passages,  where  they  enter  the  steam- 
chest,  at  O,  PL  IX.  IvK,  at  the  same  place,  are  sections  of  the 
exhaust  passages,  as  at  lik,  PL  IX.  The  arrows  will  make  the 
course  of  the  steam  intelligible.  II  is  a  three-armed  brace, 
solid  with  db,  and  alternating  with  the  centre  lines  of  the 
three  cylinders.  O  is  the  shaft ;  <?,  Babbit  metal  lining  to  the 
boxes,  dj  and  cd  are  adjusting  keys;  gf  is  a  wrought-iron 
ring,  carrying  the  guides  to  the  piston  cross-heads,  whose  outer 
ends  are  bolted  to  ears,  K. 

The  pilasters,  I,  are  fluted  in  the  original  design,  and  can 
easily  be  made  so  by  the  draftsman.  Also,  the  small  panels 
of  the  upper  part  were  finished,  as  at  m,  with  bevelled  edges  and 
round  corners. 

PL  XI.,  Fig  1,  shows  in  part  a  vertical  transverse  section 
through  the  axis  of  the  upper  cylinder ;  and  below  an  interior 
view,  with  the  end  outer  wall  of  the  frame,  between  D  and  G, 
PL  X.,  broken  away.  Thus  the  interior  of  the  cylinder,  Y,  is 
shown.  M  are  holding-down  bolts  passing  through  masonry. 
K  is  the  exhaust  pipe ;  L  and  I/  the  oblique  steam-chests, 
shown  before,  and  O  the  vertical  one,  shown  in  section.  The 
spherical  piston,  E,  being  at  the  top  of  its  stroke,  steam  is  just 
entering  from  O,  through  the  port,  j/,  and  escaping  from  below 
the  piston,  through  q  and  K.  QA  is  the  cylinder-head,  moulded 
to  conform  to  the  piston  and  the  nut  that  secures  the  piston-rod. 
The  shaded  portion,  at  gf>  is  a  section  of  one  of  the  two  wrought- 
iron  rings  which  carry  the  guides,  n. 

The  main  shaft,  S,  is  cranked,  as  shown  at  each  end  of  the 
long  crank  pin,  P,  to  the  middle  of  which  the  connecting-rod 
of  the  upper  cylinder  is  attached. 

Construction. — As  the  plan  is  only  partially  symmetrical  with 
respect  to  its  two  centre  lines,  the  only  considerable  reduction 
which  can  be  made  in  the  drawing  is,  to  make  but  half  of  the 


54  ELEMENTS    OF 

elevation,  PI.  X.  By  exercising  great  care,  these  plates  may  be 
made  on  a  scale  of  ^V  of  an  inch  to  an  inch ;  or  of  half  an 
inch  to  a  foot.  Only  the  more  important  measurements  are  re- 
corded. The  rest  may  be  determined  nearly  enough  from  the 
given  scale. 

EXAMPLE  XYIIL 
Housing  for  a  Rolling  Mill. 

Description. — PI.  XII. — This  example  presents  some  fine 
features,  both  of  construction,  and  for  practice  in  execution. 

It  was  reduced  from  designs  by  Mr.  John  Fritz,  of  Beth- 
lehem, Pa.,  for  the  mill  for  rolling  Bessemer  steel,  at  Troy,  1ST. 
Y.  The  whole  is  in  one  piece  from  H  to  I'.  It  is  here  shown 
in  plan,  two  elevations/ and  a  horizontal  section  of  the  uniform 
column. 

The  elevations  have  each  a  vertical  centre  line,  and  the  plan 
has  two.  From  these  lines  many  of  the  measurements  can  be 
laid  off. 

Several  housings  or  frames,  like  this  one,  are  ranged  in  ver- 
tical positions,  parallel  to  each  other,  and  supported  on  cast-iron 
ways,  W,W,W",  to  which  they  are  bolted  by  four  bolts,  shown 
as  at  mm'.  These  ways  are  bolted  through  oak  timbers,  20" 
wide  by  18"  deep,  to  masonry,  011  which,  in  turn,  they  rest. 

The  face  of  the  upper  part  of  the  housing,  from  aa'  to  W, 
consiots,  as  shown  in  the  plan,  of  three  vertical  cylindrical  seg- 
ments, tangent  to  each  other,  and  to  the  plane  portions  exterior 
to  aa!  and  bb'. 

The  largest  of  the  several  mouldings  on  the  outside  of  the 
housing  is  cylindrical  from  c  to  d',d",  and  double  curved  above 
d',d",  and  also  of  increasing  width  above  e,  and,  therefore,  less 
sharply  rounded,  as  its  thickness,  seen  in  front  elevation,  is 
constant. 

The  several  circles,  having  O  for  their  centre,  are  the  vertical 
projections  of  circles,  or  of  cylindrical  surfaces,  whose  axes  are 
perpendicular  to  the  vertical  plane  at  O. 

The  recesses  at  Vfg,  seen  in  the  section  at  C,  admit  the  long 
bolts,  DD.  These  bolts  are  attached,  as  at  D,  to  levers,  sus- 
pended as  at  E,  and  from  whose  inner  ends,  as  F,  depends  by 
links  the  pile  of  weights,  G,  which  contains  two  cubic  feet  of 
iron. 


MACHINE   CONSTRUCTION   AND   DRAWING.  55 

This  arrangement  is  for  use  in  plate  mills,  where  two  rolls 
are  used.  The  bearing  of  the  upper  roll,  being  clamped  to  the 
bolts  D,  would  be  drawn  up  strongly  with  the  upper  roll,  against 
the  "  top  rider "  or  covering  of  the  bearing,  over  the  roll. 
This  cover  is,  in  any  case,  held  down  by  powerful  screws  work- 
ing through  the  aperture  1,1'.  As,  then,  this  screw  bears  down 
on  the  rider  and  thence  on  the  roll,  it  acts  to  depress  the  bolts 
D  and  raise  G. 

In  the  rolling  of  rails,  etc,,  three  rolls  are  used,  and  thei 


ir 


bearings  are  confined  and  their  separation  adjusted  within  the 
recesses  E  and  E'.  Owing  to  the  immense  strain  to  which  the 
rolls  are  subjected,  which  can  best  be  realized  by  observing  how 
they  are  sometimes  broken  in  two  in  spite  of  their  great  size, 
some  yielding  point  must  be  provided  which  should  prevent  the 
breaking  of  the  rolls  by  being  a  little  weaker  than  they.  There- 
fore, a  piece,  called  a  break  piece,  is  inserted  between  the  point 
of  the  screw  which  works  through  1,1',  and  the  top  rider  or 
upper  bearing  of  the  upper  roll. 

The  wings,  as  K,K',  support  rollers  which  aid  in  handling 
the  bars  to  be  rolled.  The  apertures,  as  A,  enclose  the  bearings 
of  similar  rollers  used  in  passing  the  bars  through  the  upper 
rolls. 

Long  rods  pass  through  the  holes  at  n,n',n",  to  couple  the 
several  housings  together. 

Construction. — The  scale  of  PI.  XII.  is  T*j-.  Besides  the  fa- 
miliar directions  to  draw  as  much  as  possible  from  the  centre 
lines,  and  to  lay  down  first  the  main  outlines,  and  then  the 
smaller  parts,  the  main  features  in  the  construction  of  this 
housing  are  the  nice  union  of  its  numerous  and  crowded 
tangent  arcs,  and  the  construction  of  the  curves  as  at  Jep. 

To  secure  the  first  point,  the  pencilling  should  be  constructed 
in  the  finest  lines,  with  the  utmost  care,  and  without  wearing 
holes  at  the  centres  of  the  groups  of  concentric  arcs  ;  and  then 
they  should  be  followed  with  the  utmost  exactness  by  the  pen. 

The  scale  of  one-sixteenth  or  three-fourths  of  an  inch  to  a 
foot  is  a  very  small  one  for  such  an  object  as  is  here  described. 
Except  as  a  test  example  for  fine  drawing,  it  might  better  be 
made  on  a  double  plate  to  a  scale  of  one-eighth. 

The  construction  of  the  curves  at  kp  is  an  easy  application 
of  the  problem  of  two  intersecting  right  cylinders,  as  will  next 
be  explained.  (See  Fig.  2.) 


56  ELEMENTS   OF 

Let  AOD  be  the  horizontal  projection  of  the  segments, 
AC  and  CD,  of  two  vertical  cylinders — analogous  to  MN"  and 
K5,  in  the  plan,  Fig.  1 — tangent  to  each  other  along  a  vertical 
element  at  C.  A."D"Df  is  the  vertical  projection  of  the  same 
surface.  EFD — E'F'  is  a  cylinder  whose  axis,  EG — O',  is 
perpendicular  to  the  vertical  plane,  and  which  answers  to  a 
cylindrical  surface  having  qt'q,  Fig.  1,  for  its  vertical  pro- 
jection. ACD  and  E'C'F'  are  thus  two  projections  of  the  in- 
tersection of  these  horizontal  and  vertical  cylinders.  To  find 
the  projection  B"C"F",  answering  to  the  curves  at  leo"p  in 
the  end  view,  Fig.  1,  take  the  auxiliary  vertical  plane,  PQP', 
perpendicular  to  the  ground  line,  then  any  point,  as  CC',  being 
projected  upon  it  as  at  cc',  may  be  revolved  in  the  arc 
cc"—c'C"  to  C". 

In  like  manner,  to  find  any  points  as  o"o"  in  Fig.  1,  assume 
0,0,  in  the  plan,  project  them  upon  the  vertical  projection  of 
the  same  curves  at  0',  project  them  across  to  the  end  elevation, 
and  there  make  the  points  o"  equidistant  from  the  centre  line 
cd",  by  the  distances  of  the  same  points  o  in  the  plan,  from  the 
centre  line  nd  of  the  plan. 

In  the  plate  this  construction  is  not  followed,  as  is  evident 
upon  inspection,  since  it  would  be  very  difficult  to  draw  properly 
so  many  parallel  irregular  curves.  Besides,  it  is  fortunately  un- 
necessary, for  the  true  width  of  the  housing,  at  any  point,  is 
learned  from  the  plan,  and  the  height  at  which  any  given  width 
occurs  is  found  from  the  front  elevation.  These  curves  are  there- 
fore drawn  in  compound  circular  arcs,  as  shown,  only  the  ex- 
treme points,  as  p  and  /<-,  being  correct. 


EXAMPLE  XIX. 
A  Passenger  Car  Truck. 

Description. — PI.  XIII.,  Figs.  1 — 4:,  represents  a  four-wheeled 
passenger  car  truck  from  the  Pennsylvania  K.  R.  As  the  de- 
scription of  it  proceeds,  it  will  be  seen  to  be  very  complete  and 
well  designed,  with  abundant  provisions  for  safety  under  all  cir- 
cumstances. 

Premising  that  the  same  letters  refer  to  like  parts  on  all  the 
figures,  they  will  not  here  be  repeated  from  all  the  figures  for 
every  part. 


MACHINE   CONSTRUCTION   AND   DRAWING.  57 

Fig.  1  is  a  partial  plan.  The  right-hand  half  of  Fig.  2  is  a 
side  elevation,  and  the  left-hand  half  a  longitudinal  section 
through  the  centre.  Fig.  3  is  half  of  an  end  view,  and  Fig.  4  is 
a  cross  section  showing  the  parts  between  the  wheels. 

AA'  is  the  outer  side  beam,  and  B'  the  opposite  one.  CO'  is 
an  inner  side  beam.  DDT)"  is  the  end  transverse  beam.  EE'E" 
is  the  swinging  bar,  carrying  the  brake  shoes  W,WW,  which 
are  held  from  the  wheels  by  the  springs  UU7.  F,F'F"'  is  one 
of  two  fixed  transverse  beams,  framed  into  AA',  and  bolted 
through  C'C'.  GG'G^G'"  is  the  swinging  beam,  resting,  by 
the  block  e',e'"e'",  on  the  springs  JJ'J'",  which  bear  upon  the 
stirrup  board  H'H'",  which  is  suspended  by  the  short  diverging 
links  S'S'jS'"  from  the  hangers  I^R/jR/".  These  hangers  are 
bolted  to  the  cross  beams  FF. 

IT"  is  the  equalizing  bar,  resting  on  the  axle  boxes  M,M',M", 
which  play  up  and  down  in  the  guides  LL'L".  Between  I'  and 
A'  are  two  rubber  springs  Iv'jK'",  kept  in  place  by  a  cover  f'f" 
and  step  g'g"' ',  notched  over  the  equalizing  bar,  as  at  1!". 

NN"  are  the  wheels,  ribbed  on  the  back,  and  whose  axles, 
OO',  rest  in  the  boxes  MM'.  PP'P"  is  the  centre  bearing,  and 
T'T"  is  one  of  the  two  opposite  side  bearings  for  the  car  body. 
Q,Q'  is  a  block,  which  supports  the  iron  plate  PP'.  V V'V"  is 
a  safety  stirrup  for  catching  the  brake  bar,  EE',  in  case  of  its 
breaking  loose;  X'X"  is  a  similar  stirrup  for  holding  up  the  axle 
in  case  it  should  break.  It  often  consists  of  a  simple  bow  of 
iron  suspended  as  at  o'  and^>',  but  owing  to  the  weight  of  the  axle, 
it  is  here  strengthened  by  the  pillar  bolts  r'r'.  Y Y'  is  a  guard 
strap,  to  keep  the  beam  GG'  from  being  thrust  up  by  any  con- 
cussion, tihf'hf"  is  another  stirrup  for  catching  the  swing  board, 
II'II'",  in  case  of  accident.  ZZ'Z"  is  part  of  the  brake  gear. 
Being  drawn,  as  at  d,  by  a  chain  from  the  brake  stem  on  the 
car  platform,  it  obviously  tends  to  move  the  joints  s  and  t  as 
shown,  and  to  draw  the  brake  shoes  W,W  against  the  wheels. 

a,a'a'"  are  supports  for  the  springs  JJ'.  c,c'  is  a  saddle  plate 
under  which  the  truss  rod  W  passes.  Jckf  is  the  king  bolt  which 
holds  the  car  body  in  place  on  the  truck. 

Ideal  Conditions  and  Result. — If  the  plane  of  the  upper  sur- 
face of  the  rails  of  a  railroad  were  a  perfect  and  perfectly  un- 
yielding one,  true  as  the  ways  of  a  lathe  bed,  if  the  track  were 
perfectly  straight,  and  if  the  circularity  and  equality  of  the 
wheels  were  perfect,  the  motion  of  every  point  of  a  car  would  be 


58  ELEMENTS   OF 

one  of  perfect  translation,  and  would  be  as  easy  with  no  springs, 
or  yielding  parts  of  any  kind  in  the  running  gear,  as  with  them. 

Actual  Conditions. — Xone  of  the  above  conditions  perfectly 
exist.  The  actual  variations  from  perfect  circularity  and  equali- 
ty in  the  wheels  are,  however,  insensible,  compared  with  the  de- 
fects in  the  other  respects,  and  may  be  neglected.  But  the  track, 
taking  the  centre  line  of  each  rail  for  reference,  exhibits  both 
vertical  and  lateral  variations  from  a  straight  line.  The  former 
may,  further,  be  simultaneous  in  the  two  rails,  as  in  the  depres- 
sion at  the  joints  of  tracks  whose  joints  fall  on  the  same  cross 
ties,  and  may  be  equally  or  unequally  so  ;  or  they  may  be  alter- 
nate, as  in  case  of  tracks,  often  seen  at  present,  in  which  the 
joints  fall  on  different  ties,  half  the  length  of  the  rail  apart. 

Lateral  deviations  may  also  be  simultaneous  or  irregular, 
equal  or  unequal ;  and  in  both  kinds  of  variations  there  may  or 
may  not  be,  though  there  generally  is,  a  return  to  the  line  departed 
from.  Finally,  owing  to  these  irregularities,  the  surface  deter- 
mined by  the  tops  of  the  rails  is  neither  a  perfect  nor  an  un- 
yielding plane. 

General  Idea  of  Rolling  Gear. — This  is,  to  secure  in  all  the 
yielding  points  of  the  truck  easy  and  brief  oscillations  about 
mean  points,  so  that  for  a  given  vertical  and  lateral  unevenness 
of  track,  every  point  of  the  line  of  support,  T"P",  and  hence  the 
car  body,  shall  move  as  nearly  as  possible  with  as  pure  motion  of 
translation,  when  the  track  is  straight,  as  it  would  do  under  the 
ideal  conditions  above  stated. 

Normal  Condition  of  Springs. — Let  a  sixty-seat  car  be  loaded 
with  fifty  people,  for  example,  for  a  given  journey,  and  be  stand- 
ing still.  All  the  springs  will  then  be  compressed  with  what  we 
will  call  their  normal  compression  for  that  time.  This  degree 
of  compression  would  remain  constant  under  the  ideal  conditions 
already  mentioned. 

Action  under  Actual  Conditions. — The  car  body  rests  on  the 
swing  beam  GG'G",  at  the  three  points,  P",  and  the  two  of 
which  T"  is  one.  This  beam  rests  on  the  springs,  J,  on  both 
sides  of  the  truck  ;  and  there,  on  the  swing  board,  H'lF",  which 
hangs  by  the  links,  S',  and  hangers,  B/,  from  the  cross  bars, 
FF,  of  the  rigid  frame  of  the  truck.  This  frame  rests  on  the 
four  rubber  springs,  of  which  K'  is  one ;  these  upon  the  equaliz- 
ing bars  as  F,  and  these,  finally,  on  the  axle  boxes,  MM',  which 
bear  upon  the  tops  of  the  axles  OO'.  The  last  are  a  final  rigid 


MACHINE   CONSTRUCTION  AND   DRAWING.  59 

support,  being  practically  solid  with  the  wheels  which  roll  upon 
the  track. 

l^ow  let  qn,  Fig.  2,  be  the  top  of  a  rail  depressed  at  the  joint 
q  by  the  distance  mn,  exaggerated  for  illustration.  When  a 
train  is  at  full  speed,  the  point  at  n  of  the  wheel  is  going  hori- 
zontally, at  from  40  to  70  feet  per  second.  Hence  the  rise,  mn, 
is  practically  instantaneous,  and  nearly  the  same  as  if  the  wheel 
were  thrust  up  the  same  distance  by  the  impact  of  a  violent 
blow  from  below.  Then,  when  n'  thus  instantly  rises,  a  small 
distance ;  M',  and  the  end  of  the  bar  I',  rise  the  same  distance, 
which  compresses  the  spring  K'.  Now,  if  the  force  and  quick- 
ness of  the  rise  are  no  more  than  enough  to  compress  the  spring, 
the  truck  frame,  A  A",  &c.,  will  be  undisturbed  ;  but  if  the  up- 
ward action  be  not  all  taken  up  by  the  spring,  the  truck  frame 
will  be  raised  by  the  excess  of  that  action,  and  will,  through 
RB/  and  S',  draw  up  the  swing-board  H'H'",  and  compress  the 
steel  springs  JJ'.  If,  also,  this  excess  of  upward  action  be  not 
all  spent  on  the  springs  JJ',  the  swing-beam,  GG',  and  the  car 
body  will  be  raised  a  little. 

We  now  see  that  with  no  springs  the  car  body  would  sensibly 
be  raised  as  far  and  as  suddenly  as  the  wheel  at  n'.  But  with 
springs,  if  lifted  at  all,  the  motion  will  be  comparatively  easy 
and  gradual,  through  the  gradual  action  of  the  springs,  in  their 
compression  and  expansion,  till  again  in  equilibrium. 

Let  us  now  consider  the  effect  of  lateral  shocks.  A  sidewise 
lurch  of  the  truck  to  the  left,  for  example,  will  carry  all  its 
rigid  parts,  A^R^F'",  etc.,  Fig.  4,  to  the  left.  This  will  carry  the 
points  of  suspension,  u,  of  the  links  to  the  left,  which  will  make 
the  left-hand  link  more  vertical,  and  the  link  S'"  more  oblique 
than  now.  Equilibrium  will  thus  be  destroyed ;  and  the  links, 
in  coming  to  equilibrium  by  returning  to  an  equal  inclination 
to  a  vertical  direction,  will  carry  H'",  and  with  it  the  springs 
J//;,  and  the  swing-beam  G"',  and  car  body. 

Trucks  are  very  often  made  with  the  top  of  G"f  no  higher 
than  the  top  of  Fx//,  and  with  the  links  S'"  then  swung  from  an 
axis  resting  on  top  of  FFjF'F'",  and  reaching  from  that  to  o'". 
In  such  a  case,  the  links  are  usually  vertical,  also ;  so  that  the  os- 
cillations would  be  slower,  by  reason  of  the  length  of  the  links, 
but  -longer,  owing  to  the  less  upward  component  of  motion  in 
an  arc  of  longer  radius.  The  shortness  and  convergence  up- 
wards of  the  links  in  the  present  design  would,  we  should 


60  ELEMENTS   OF 

think,  make  the  truck  quite  stiff,  though  properly  so,  in  respect 
to  lateral  oscillation ;  and  not  too  much  so  for  a  smooth  and 
firm  track. 

This  descriptive  statement  of  the  theory  of  the  four-wheeled 
car-truck  is  all  that  could  well  be  given,  for  there  could  hardly 
be  a  clearer  example  of  a  piece  of  mechanism  whose  proportions 
must  be  determined  experimentally,  since  the  numberless  varia- 
tions in  the  intensity  and  direction  of  the  forces  applied  would 
seem  to  make  a  mathematical,  that  is,  an  exact  quantitative 
investigation  impossible. 

Six  and  Eight-wheeled  Trucks. — The  idea  of  both  is  the  same, 
viz. :  to  secure  a  perfect  rectilinear  motion  to  the  car-body,  by 
having  all  the  irregular  wheel-motions  occasioned  by  the  track 
taken  up  within  the  truck  itself.  In  the  eight-wheeled  truck  a 
heavy  intermediate  timber  frame,  or  carriage,  rests  on  two  com- 
mon trucks,  and  the  car-body  on  the  middle  transverse  line  of 
this  carriage,  where  there  is  almost  no  jarring  motion.  In  the 
six- wheeled  truck  the  same  end  is  not  quite  so  fully  accomplish- 
ed, since  there  is  one  rigid  frame  as  in  the  four-wheeled  truck, 
and  the  intermediate  carriage  is  shorter ;  but  there  are  two 
swing-beams,  one  on  each  side  of  the  middle  pair  of  wheels, 
and  a  small  carriage-frame  rests  on  the  two  beams,  while  the 
car-body  rests,  as  before,  on  the  transverse  centre  line  of  this 
carriage. 

In  respect  to  these  trucks,  it  may  be  said  that,  though  a  per- 
fect track  costs  a  good  de'al,  yet  the  difference  between  that  of 
a  smooth  and  a  rough  one  may  be  small,  as  compared  with  the 
cost  of  eitlier,  and  the  extra  cost  of  compound  trucks,  at  first, 
and  for  repairs,  and  of  the -extra  motive  power  required  to 
transport  them,  might  go  far  to  cover  this  difference. 

Car  Cross-sections. — While  on  this  subject,  it  seems  appro- 
priate, from  association,  to  mention  two  great  points  of  car- 
moving  economy,  one  of  which  seems  to  be  more  and  more 
overlooked.  These  are,  the  steadily  increasing  size  of  the 
cross-section  of  the  car,  and  the  distance  between  the  cars.  A 
part  of  the  needless  extravagance  of  the  times  is  the  indiscrimi- 
nate carrying  of  the  luxury  of  high  rooms  to  live  in,  into 
vehicles  to  travel  in,  as  if  travelling  about  were  the  normal 
condition  of  one's  life ;  and  forgetting  the  needless  and  great 
waste  of  means  in  dragging  100  square  feet  of  car  end,  includ- 
ing truck  surface,  at  40  miles  an  hour  through  the  air,  when  70 


MACHINE   CONSTRUCTION   AND   DRAWING.  61 

would  do  just  as  well,  and  afford  every  essential  comfort.  Side- 
doors  opening  outward  are  dangerous ;  in  one  way  if  locked, 
and  in  another,  if  unlocked.  If  opening  imoard  they  waste  room. 
Hence,  end-doors  and  the  centre-aisle  seem  best,  as  well  as 
hardly  to  be  dispensed  with,  as  affording  the  comfort  of  a  free 
inside  passage  through  the  train.  But,  observing  that  perhaps 
more  travel  singly  or  in  threes  than  in  pairs,  cars  might  be  bet- 
ter filled,  as  well  as  economically  narrowed,  by  having  a  row  of 
single  seats  on  one  side  of  the  aisle.  Then,  as  to  height  of  car, 
who  has  not  felt  cold  feet  while  the  thermometer  would  be  at 
100°  to  110°,  at  the  ceiling  of  a  car  7£  or  8  feet  high  ?  Let  the 
car  be  heated  by  water-pipes  at  the  passengers'  feet,  and  com- 
ing from  heaters  under,  or  in  open-screened  compartments  in 
the  end  of  the  car ;  and,  with  suitably  screened  ventilators,  6£ 
feet  would  be  high  enough  for  a  car  inside.  Thus,  the  cross- 
section  of  the  car-body  might  be  reduced  to  only  about  60 
square  feet ;  which  is  a  great  matter,  when  it  is  considered  that 
the  resistance  of  the  atmosphere  exceeds  the  sum  of  all  other 
resistances  on  a  level,  at  speeds  of  30  miles  an  hour  or  more  ; 
and  that  it  increases  a"t  least  as  the  square  of  the  velocity  of  the 
train,  so  as  to  "be  four  times  as  great  for  twice  the  velocity. 

Again,  when  the  space  between  the  cars  is  equal  to  the  width 
of  the  car  or  more,  the  resistance  of  the  atmosphere  to  each  car 
after  the  first  one,  is  from  seven-tenths  to  nearly  as  great  as 
it  is  to  the  first  one.  Hence,  the  platforms  should  be  enclosed 
by  painted  canvas,  or  by  permanent  walls,  with  end  and  side 
doors,  the  latter  to  be  opened  just  before  arriving  at  stations  by 
the  train  operatives.  The  car  ends,  having  also  suitably  adapt- 
ed couplings,  might  be  thus  not  more  than  one  foot  apart  in- 
stead of  eight  or  ten  .as  now,  and  with  great  economy  of  power. 

The  sums  saved  by  these  arrangements  being  spent  upon  the 
track,  fencing  and  flagmen,  the  increased  smoothness  and  safety, 
together  with  the  diminished  train-surface  exposed  to  air-resist- 
ance, would  allow  increase  of  speed  without  increase  of  cost 
over  present  results ;  and  this,  by  saving  time,  would  be  real 
economy,  inasmuch  as  trains  and  travellers  are  not  producers. 

Reduction  of  Car  Weight. — Once  more,  we  must  mention  the 
enormous  dead  weight  of  train,  including  the  engine,  for  each 
passenger,  even  of  a  fully  filled  train.  This  weight  is  not  far 
from  1,500  pounds  per  passenger.  To  materially  reduce  this 
most  power-wasting  excess,  it  may  be  best  to  return  to  an 


62 

essential  feature  of  Nature's  works ;  since  the  more  truly  they 
are  imitated  in  man's  constructions,  the  more  perfect  the  latter 
will  be.  This  feature,  or  principle,  is,  that  Nature's  great  con- 
structions are  aggregations  of  many  small  ones,  in  the  form  of 
minute  cells. 

In  other  words :  component  parts  should  be  small  and  hol- 
low. Applying  this  principle  to  a  car,  its  frame  might  well  be 
composed  of  sheet-iron  cell-work,  prismatic  or  cylindrical. 
Applying  it  to  the  train  as  a  whole,  the  superior  strength  of  a 
small  cell,  to  a  large  one  with  equally  thick  walls,  would  point 
to  the  adoption  of  small  light  cars,  or  of  numerously  partitioned 
large  ones. 

As  the  enormous  dead  weight  of  a  train  is  bodily  lifted 
through  the  vertical  height  of  every  gradient  on  the  line  tra- 
versed by  it,  while  friction  is  the  only  car  resistance,  on  a  level, 
it  may  well  repay  railroad  companies  to  make  ample  experi- 
ments, founded  on  these  considerations,  with  a  view  to  the 
greatest  possible  reduction  of  car-weight  per  passenger. 

Construction. — By  an  oversight,  the  horizontal  heavy  lines  of 
the  plan  were  placed  on  the  lower  edges  of  the  several  pieces  of 
the  truck.  This  is  the  English  fashion,  but  it  supposes  two  dif- 
ferent directions  of  light,  one  for  the  plan  and  another  for  the 
elevation. 

The  circles  with  cross-marks  in  them  are  washers,  with  nuts 
only  indicated,  not  shown. 

If  desired,  the  scale  could  be  enlarged  to  one  inch  to  one 
foot,  and  the  cross-section  could  be  placed  side  of  the  end  view, 
to  facilitate  its  construction. 


MACHINE   CONSTRUCTION   AND   DRAWING.  63 


CLASS  IL-RECEIYERS. 

57.  In  any  machine  there  is  a  piece,  which  is  the  first  in  the 
order  of  mechanical  succession,  it  being  the  one  to  which  the 
motive-power  is  first  applied.  Such  a  piece  is  called  a  re- 
ceiver. 

In  a  vast  number  of  instances,  the  receiver  is  a  band-wheel. 

When  many  machines,  as  the  looms  of  a  cotton-mill,  or  the 
lathes,  planers,  etc.,  of  a  machine-shop,  receive  their  motion 
from  an  overhead  line  of  shafting,  which  constantly  revolves, 
it  is  important  to  stop  any  one  or  more  of  those  machines 
at  pleasure,  without  compelling  the  rest  to  stop.  For  this  pur- 
pose, the  band-wheel  receiver  is  double,  that  is,  two  equal  band- 
wheels  play  side  by  side  upon  the  same  shaft ;  but  one  is  fast  to 
the  shaft  and  the  other  loose,  so  that  when  the  band  from  the 
overhead  pulley  is  shifted  to  the  loose  pulley,  the  machine  stops. 
In  some  cases  the  fast  and  loose  pulleys  are  on  the  line  of  shaft- 
ing. 

Another  very  common  form  of  receiver  is  a  piston,  whether 
in  steam,  gas,  air,  or  water  engines. 

Other  forms  of  receivers  are  named  in  the  general  table. 

A— Point  Receivers. 
B— Line  Receivers. 

Of  these  it  has  not  seemed  necessary  to  present  any  figures. 

C— SURFACE    RECEIVERS, 
a — Plane  Receivers. 

EXAMPLE  XX. 
Locomotive  Piston  with  RoiKs  Steam-piston  Packing. 

Description. — This  piston-packing,  PL  III.,  Figs.  4 — 8,  is  made 
to  pack  the  cylinder  of  any  engine,  or  pump,  uniformly,  and  no 
more  tightly  at  any  given  pressure  than  is  necessary ;  creating 


C4  ELEMENTS   OF 

little  or  no  friction.  It  embraces  certain  novel  improvements 
in  that  class  of  packing  for  pistons,  which  is  composed  of  me- 
tallic sections,  forming,  when  put  together,  expansible  rings 
which  are  applied  within  annular  recesses,  formed  in  the  cir- 
cumference of  a  piston,  so  that  when  acted  upon  by  steam,  the 
sections  of  a  ring  will  be  forced  out  against  the  inner  surface 
of  the  cylinder  and  thereby  pack  the  piston.  In  this  class  of 
pistons,  the  steam  acts  upon  the  packing  from  the  inside  out- 
ward, provision  being  made  for  the  passage  of  the  steam  into 
chambers  formed  on  the  piston,  and  thence  through  an  outer 
ring,  which  receives  the  packing-rings. 

The  main  object  of  this  invention  is,  to  construct  and  apply 
sectional  packing-rings  to  a  piston,  so  that  advantages  shall  be 
secured  superior  to  those  heretofore  attained  in  that  class  of 
pistons  which  have  their  packing  expanded  by  steam. 

Another  object  of  this  invention  is,  to  provide,  in  horizontally 
working  pistons,  against  an  unequal  wearing  away  of  the  same, 
by  the  application  of  an  elastic  plate  to  that  part  of  the  piston 
which  slides  on  the  lowest  point  of  the  interior  of  the  cylinder, 
which  plate  compensates  for  the  extra  wear  caused  by  the 
weight  of  the  piston. 

There  have  been  in  use  many  patent  piston  packings,  that 
have  proved  to  be  in  some  cases  superior  to  the  ordinary  metallic 
packing,  in  so  far  as  they  have  saved  labor  in  packing  the  piston. 
In  other  cases  they  have  proved  to  be  inferior  to  the  ordinary 
packing,  particularly  when  an  engine  has  been  run  to  its  full 
capacity.  The  reason  of  this  is,  that  in  all  such  pistons  the 
whole  inner  surface  of  the  piston  is  exposed  to  the  pressure  of 
steam  in  the  cylinder,  and  this  high  pressure  causes  too  much 
friction,  consequently  wearing  away  the  cylinder  and  packing- 
rings  unnecessarily  fast. 

Some  kinds  of  packing-rings  are  in  sections,  which  adjust 
themselves  to  the  inner  surface  of  the  cylinder  at  a  very  small 
pressure,  but  at  a  pressure  of  from  100  to  150  pounds  to  the 
square  inch  cause  so  great  friction  as  to  waste,  it  is  said,  from  10 
to  20  per  cent,  of  the  power  of  the  engine. 

In  other  cases,  where  the  packing-rings  are  cut  only  once, 
those  rings  have  to  be  tolerably  thin,  so  as  to  spring  out  to 
the  inner  surface  of  the  cylinder,  at  ordinary  pressure,  and 
are  therefore  easily  broken  in  case  there  are  any  flaws  in 
them. 


MACHINE   CONSTRUCTION   AND   DRAWING.  65 

In  almost  all  such  pistons  there  is  a  solid,  or  uncut  guide 
ring,  which  has  to  be  fitted  as  nearly  as  possible  into  the  cylin- 
der ;  but  in  horizontal-working  pistons  this  ring  wears  more  or 
less  on  its  lower  side,  and,  in  course  of  time,  throws  the  piston 
out  of  the  centre  of  the  cylinder,  which  causes  an  uneven  wear 
to  the  piston-rod,  stuffing-box,  guides,  and  cross-head.  All  these 
evils  are  avoided  in  this  piston,  thus : — 

1st.  The  rings  are  very  strong,  much  broader,  and  have  only  a 
small  part  of  surface  of  the  packing  rings  exposed  to  the  steam 
(water  or  air). 

2d.  By  a  peculiar  and  simple  contrivance,  when  an  engine  is 
running  with  steam,  the  pressure  on  the  lower  part,  between 
the  piston  and  part  of  the  packing,  causes  the  piston  to  balance, 
or  force  it  somewhat  off  the  bottom  of  the  cylinder.  When 
steam  is  shut  off,  an  elastic  plate  on  the  bottom  of  the  piston, 
which  is  pressed  out  by  a  spring  or  set  screw,  or  both  combined, 
answers  the  same  purpose. 

The  packing  rings  are  cut  in  not  less  than  three  pieces,  but 
this  depends  upon  how  true  the  cylinder  is.  When  the  packing 
is  put  into  cylinders  that  are  out  of  round  and  not  parallel,  it 
is  better  to  cut  the  rings  into  more  pieces,  that  they  may  adjust 
themselves  better  to  the  irregular  form  of  the  cylinder. 

3d.  In  locomotives  running  with  from  100  to  150  pounds  of 
steam,  and  whose  cylinders  are  true,  one-eighth  inch  steam 
bearing  under  the  packing  rings  is  all-sufficient ;  on  worn 
cylinders  one-fourth  to  three-eighths  of  an  inch  may  be  neces- 
sary at  first,  afterwards  it  can  be  reduced  to  one-eighth  and  less. 
The  surface  of  the  rings  bearing  against  the  surface  of  the 
cylinder  can  be  quite  broad ;  the  friction  will  be  no  more,  and 
they  last  longer  in  proportion  to  their  width.  These  rings  must 
be  fitted  very  closely,  and  must  not  have  more  play  than  will 
permit  them  to  barely  move  between  spider  and  follower. 

Fig.  4  is  a  section  through  the  axis  of  the  piston  rod. 

Fig.  5  is  an  end  view  of  the  piston,  with  the  follower 
removed. 

Fig.  6  is  a  diametrical  section  through  the  central  ring. 

Fig.  7  is  a  central  section  through  central  ring,  perpendi^ 
cular  to  the  axis  of  the  cylinder. 

Fig.  8  is  a  diametrical  section  through  packing  rings. 

A  and  B  constitute  the  body  of  the  piston,  A  being  the 
"  spider,"  and  .B  the  follower,  which  parts  are  constructed  and 
5 


66  ELEMENTS   OF 

bolted  together  in  the  usual  manner,  as  shown.  When  these 
two  parts  are  bolted  together,  they  form  an  annular  space 
between  their  flanges  for  the  reception  of  the  central  ring 
C,  which  is  supported  by  the  ends  of  radial  arms  of  the  portion 

A,  so  as  to  lap  over  the  joint  of  the  two  parts  AJB,  as  shown  in 
Fig.  4,  and  thus  prevent  the  entrance  of  steam  in  the  body  of 
the  piston.     This  ring,  O,  is  fitted  so  as  to  be  steam  tight  and 
immovable,  when  screwed  between  the  spider  A,  and  follower 

B.  The  ring,  C\  has  a  central  rib  which  leaves  on  each  side  of 
it  an  annular  space  for  receiving  the  expansible  packing  rings. 
This  centre  ring,  (7,  forms  one  side  for  each  expansible  ring  (the 
inner  side),  the  other  side  being  formed  by  the  circular  flanges 
of  the  piston  as  shown  in  Fig.  4.     The  inner  corners  of  the 
circular  flanges  of  the  piston  are  bevelled  as  shown  at  aa  for 
receiving  the  corresponding  bevelled  surface   of  the   packing 
rings  bb,  portions  of  which  are  closely  fitted  within  the  annular 
chambers  above  described,  so  that  their  circumferences  project 
a  short  distance  beyond  the  circumference  of  the  piston.     The 
packing  rings  bb  are  made  up  of  segments  or  sections,  and  are 
held  out,  so  that  their  outer  surfaces  press  gently  against  the 
inner  surface  of  the  steam  cylinder,  by  means  of  springs  cc,  the 
ends  of  which  are  bent  outward,  as  shown  in  Fig.  5,  so  as  to  act 
upon  the  ends  of  the  segments  bb,  and  thus  to  keep  the  ends  of 
all  the  segments  snugly  together,  except  those  segments  between 
which  the  springs  are  bent  outward.     These  springs,  cc,  not  only 
act  to  expand  the  sectional  packing  rings,  but  they  also  operate 
to  keep  the  ends  of  the  sections  together  so  as  to  form  tight 
joints.     To  prevent  the  entrance  of  steam  within  the  chambers 
between  the  sections,  5,  and  the  flanges  of  central  ring  C,  there 
are  recesses  in  the  ends  of  those  segments  which  receive  the  ends 
of  the  springs,  cc,  and,  inserted  into  said  recesses,  short  pieces, 
G,  which  break  joints  with  the  joints  of.  said  segments.     The 
segments  Gr  may  be  screwed,  or  riveted  to  the  segments  b  on 
one  side  of  the  joint.     For  horizontal  working  pistons,  where 
the  weight  of  the  piston  is  supported  upon  the  lower  inner 
surface  of  the  cylinder,  there  is  a  segment,  g,  which  is  inserted 
into  a  recess  formed  in  the  ridge  of  ring  C,  and  acted  upon  by 
a  spring  or  set  screws,  ra,  or  both  combined,  which  supports,  or 
nearly  supports,  the  weight  of  the  piston  upon  said  piece  g. 
This  piece,  g,  may  be  made  of  hard  brass  or  any  other  suitable 
metal,  and  as  its  outer  surface  wears  away,  the  spring  will 


MACHINE    CONSTRUCTION   AND   DRAWING.  67 

force  it  outward,  or,  from  time  to  time,  it  can  be  set  out  in  proper 
place  by  set  screws,  m,  so  that  the  axis  of  the  piston,  and  axis  of 
the  cylinder,  within  which  the  piston  works,  will  always 
coincide.  This  will  prevent  the  piston,  stuffing  box,  and  its 
rod,  from  wearing  untrue.  Where  the  weight  of  the  piston  is 
supported  by  the  piston  rod,  as  in  upright  cylinders,  the  piece 
<7,  with  springs  and  set  screws  m,  can,  and  should  be  dispensed 
with.  It  will  be  seen  by  reference  to  Fig.  4,  that  the  cir- 
cumference of  the  packing  rings  projects  sufficiently  beyond 
the  circumference  of  the  piston  flanges,  to  allow  steam  to  pass 
those  flanges,  and  act  upon  the  projecting  bevelled  surfaces  of 
the  packing  rings,  and  expand  them  against  the  surface  of  the 
cylinder  with  a  pressure  commensurate  with  the  force  of  steam. 
The  springs,  cc,  are  designed  merely  to  keep  the  packing  rings 
expanded  and  in  position  to  be  acted  upon  by  steam,  and 
forcibly  expanded  thereby.  This  invention  is  not  confined  to 
steam  engine  pistons,  as  it  is  applicable  to  pistons  for  air  and 
water  engines.  The  segments  t>  may  be  made  rectangular,  or 
of  other  suitable  shape,  in  cross  section. 

Construction. — 16  ins.  may  be  assumed  as  the  diameter  of 
this  piston,  and  it  may  then  be  drawn  on  a  scale  of  one-sixth, 
showing  a  little  more  than  half  of  Figs.  5  and  7. 


EXAMPLE  XXI. 

Thirty-six  and  Fifty-four-inch  Pistons. 

Description. — In  PI.  XI.,  Fig.  1,  R  represents  a  vertical  sec- 
tion of  a  piston,  with  partly  spherical  upper  and  under  surfaces. 
All  of  its  horizontal  sections  being  circles,  a  plan  view  of  it 
could  easily  be  added,  to  make  a  separate  example. 

PI.  IV.,  Fig.  3,  represents  a  fifty-four-inch  propeller  engine 
piston ;  KHJ>  is  half  of  the  part  called  the  " spider"  and 
H'A'K'  a  vertical  section  of  it  on  KII,  so  that  all  below  A'B', 
except  E'^D'  and  F'G',  should  be  filled  with  shading  lines. 
The  correspondence  of  the  letters  will  show  the  relative  heights 
«f  the  different  points  above  A'e".  Thus,  the  tops  of  the  arms 
•and  rim,  5,  ae,  A,  are  in  the  plane,  D'l'.  LM  is  the  cover 
which  closes  on  to  the  spider,  its  under  face  resting  on  the  plane, 
DT.  The  bore  for  the  piston  rod  is  slightly  conical. 


DO  ELEMENTS   OF 

In  the  annular  space,  H'GT,  between  the  spider  bottom  and 
the  cover,  is  inserted  the  packing.  Formerly  this  consisted  of 
two  or  more  rings  cut  once  or  more,  so  as  to  be  adjustable  to 
the  inner  surface  of  the  cylinder,  and  breaking  joints,  so  that 
the  cuts  not  lying  together,  steam  could  not  pass  through  them 
from  one  side  of  the  piston  to  the  other.  These  rings  were  then 
set  out  by  springs,  bearing  on  the  inside  of  the  rings,  and 
pressed  against  the  rings  by  screws  bearing  at  their  inner  ends 
against  some  of  the  unyielding  parts  of  the  piston. 

At  present  steam-packing  is  very  generally  used.  In  this 
example,  OO'  is  a  part  of  the  skeleton  ring,  resting  against 
the  outer  ends,  IJ,  of  the  spider  arms,  n'n'  •  n,  N  show-s,  the 
packing  itself,  consisting  of  two  rings,  of  which  the  inner  one,  f" 
square  in  section,  fits  within  the  other,  as  at  n',  n".  Shallow  cuts 
filed  away,  as  atj^  admit  the  steam  over  the  edges  of  the  piston 
body,  which  does  not  quite  fit  the  cylinder,  into  the  space  be- 
tween the  skeleton  ring,  O',  and  the  packing.  Steam  can  also 
be  admitted  through  small  holes  through  the  piston  bottom  and 
cover,  near  their  edges. 

Construction. — A  larger  section  of  the  packing,  on  a  scale  of 
i  or  ^,  might  be  made,  including  the  adjacent  parts  of  the 
piston  body. 

b — Developable  Receivers. 

EXAMPLE  XXII. 
A  Fourneyron  Wheel  Plan. 

Description. — This  example,  PL  IY.,  Fig.  5,  does  not  include 
the  finished  wheel,  but  only  what  is  most  essential,  viz. :  the 
laying  out  of  the  bucket  and  guide  curves,  as  seen  in  plan, 
where  their  true  curvature  is  shown.  O,  near  the  bottom  of 
the  plate,  is  the  centre  of  the  wheel,  whose  extreme  radius  is 
49£  ins. ;  radius  to  outer  ends  of  buckets,  49  ins.,  and  to  their 
inner  ends,  40  ins.  There  are  44  buckets,  8J  ins.  apart  at  the 
outer  edges,  and  /¥  of  an  inch  thick,  made  of  polished  Russia 
iron. 

The  water  enters  the  wheel  from  above,  through  a  trunk  of 
nearly  the  same  diameter  as  the  inner  radius  of  the  wheel,  filling 
the  guide  channels,  and  issuing  thence  against  the  buckets,  and 
producing  rotation  in  the  direction  of  the  arrow.  As  the  wheel 


MACHINE   CONSTRUCTION   AND   DRAWING.  69 

gives  way  by  its  revolution  from  before  the  water,  the  latter 
does  not  bend  round  and  run  out  as  if  in  a  fixed  channel,  AGBE, 
but  goes  directly  on,  as  indicated,  in  a  general  way,  by  the  lines 
KM  and  AN,  carrying  the  bucket  with  it,  and  hence  the  wheel. 
Still,  as  a  particle  of  water,  relatively  to  the  bucket,  follows  its 
curve,  AFB,  the  form  of  the  bucket  is  not  a  matter  of  in- 
difference. 

The  guides  are  fixed,  and  their  number  somewhat  arbitrary, 
but  usually  taken  at  from  half  to  three-fourths  the  number  of 
buckets.  To  avoid  the  injurious  pulsation  which  might  follow 
if  many  guide  edges  should  coincide  at  once  with  bucket  edges, 
it  is  doubtless  best  to  have  the  bucket  and  guide  numbers  prime 
to  each  other,  that  is,  with  no  common  divisor  except  1. 
Hence  we  have  proposed  31  guides  to  44  buckets  in  the  present 
example. 

The  regulating  gate  is  a  vertical  thin  cylinder,  which  shuts 
vertically  downward  in  the  annular  space,  II  Gr,  all  around  the 
wheel,  between  it  and  the  guides.  Water,  therefore,  enters 
the  guide  passages  throughout  the  entire  circumference  of  the 
guide  case,  deducting  only  the  thickness  of  the  guides  them- 
selves ;  while  in  the  Jonval  wheel  the  guide  openings,  as  they 
would  be,  without  a  gate,  are  half  closed  by  the  gate.  This,  how- 
ever, is  not  an  essential  point,  for  in  both  cases  water  issues 
against  the  bucket  from  the  entire  outer  circumference  of  the 
guide  case,  with  the  above  deduction,  and  ;iie  whole  structure 
can  be  designed  with  such  dimensions  as  to  give  any  desired 
area  of  guide  opening. 

Construction. — With  a  scale  of  one-tenth,  describe  the  princi- 
pal circumferences  with  the  dimensions  given.  The  circum- 
ference containing  the  bucket  ends,  divided  by  the  number  of 
buckets,  will  give  the  distance  BE.  The  shortest  distance,  EF, 
between  the  buckets  being  fixed  by  the  designer,  the  following 
form  and  construction  has  been  proposed  :  Put  EF=#,  and  the 
thickness  of  the  bucket=5.  Make  BC=5«,  and  draw  the  ra- 
dius, CO,  to  determine  A,  the  inner  end  of  the  bucket.  Draw 
AD,  tangent  to  the  circle  OA,  and  the  arc  E-F,  with  a  radius 
equal  to  a  +  b.  Then  the  direction  of  B«  must  be  found  by 
trial,  so  that  AD  being  marked  on  the  edge  of  a  slip  of  paper, 
shall  be  applied  with  D  always  on  B«,  and  the  segments  te,  or 
rF,  etc.,  constant  nnd  equal  to  BD.  «BO  may  vary  from  10°  to 
12°.  Otherwise,  alter  the  length  of  BC.  The  curve  thus  pass- 


TO 


ELEMENTS    OF 


ing  through  A<$,  etc.,  should  be  just  tangent  to  EF,  and  will 
be  the  inner  face  of  the  bucket.  If  it  be  not  so,  assume  a 
new  position  for  Ba. 

For  the  guide  curves,  describe  the  arc,  K— -f,  with  the  least 
opening  of  the  guides  for  a  radius,  and  H<7  with  double  this  ra- 
dius. Then  describe  hg,  through  h,  and  tangent  to  the  two  arcs 
just  noted.  This  can  easily  be  done  by  trial ;  determining  the 
centre  P  (in  Fig.  3).  This  gives  the  essential  portion  of  the 
guide  curve.  The  remainder,  gk,  is  drawn  from  any  conve- 
nient centre,  as  Q,  such  that  gk,  produced,  would  pass  through 
the  centre,  O,  of  the  wheel. 


The  centres  for  all  the  other  guide  curves  corresponding 
with  hg  will  be  on  the  circle  with  radius  OP,  and  those  for  the 
curves  of  which  gk  is  one,  will  be  on  the  circle  with  ra- 
dius OQ. 

The  above  figure,  21,  will  give  a  sufficient  idea  of  the  general 
arrangement  of  parts.  A  is  the  wheel  plate,  keyed  to  the  shaft 
G,  by  a  collar  B,  and  bearing  the  vertical  buckets,  E,  on  its 
outer  rim.  CD  is  the  fixed  guide  bottom,  carrying  the  guide 
curves,  of  which  HID  represents  one.  F  is  a  fragment  of  the 
thin  cylindrical  gate,  shown  partly  open,  which  lifts  out  of  the 
annular  space  between  the  guides  and  buckets,  and  admits  the 
water  from  above  through  the  trunk,  to  the  guides,  and  thence 
through  the  buckets  as  shown  by  the  arrows. 


MACHINE   CONSTRUCTION   AND   DEAWING.  71 

o — Warped  Receivers. 

EXAMPLE  XXIII. 
A  Jonval  Turbine   Wheel  and  Bucket. 

58.  Introductory  Explanations. — Water  wheels  may  be  clas- 
sified as  vertical  and  horizontal.  The  former  have  horizontal 
axes ;  the  latter,  as  in  the  last  example,  have  vertical  ones. 

Vertical  wheels  are  overshot,  undershot,  or  breast  wheels. 
These  are  so  generally  figured  in  the  elementary  books,  or  ex- 
emplified along  many  mill  streams,  as  not  to  need  illustration 
here.  Overshot  wheels  are  those  to  which  the  water  is  delivered, 
at  or  near  their  highest  part,  into  trough-shaped  buckets,  deep 
and  narrow,  so  as  to  retain  the  water  longer.  It  escapes  at  or 
near  their  lowest  line.  Thus  all  the  buckets  on  one-half  of  the 
wheel  aie  loaded  with  water,  the  unbalanced  weight  of  which 
causes  it  to  descend,  and  the  wheel  to  revolve. 

Undershot  wheels  are  like  the  paddle  wheels  of  a  steamboat ; 
armed  with  floats  at  the  circumference,  parallel  to  the  axis,  so 
as  to  be  acted  upon  by  water  rapidly  running  against  them. 
They  of  course  utilize  but  a  very  small  part  of  the  power  of  the 
water,  but  can  be  improved  by  curving  or  inclining  the  floats 
up  stream. 

Breast  wheels  are  those  to  which  the  water  is  delivered  at  or 
near  the  height  of  their  axes.  They  may  have  buckets  like  an 
overshot  wheel,  or  floats  like  an  undershot,  but  moving  with 
their  outer  edges  very  near  to  a  curved  apron  of  wood  or  stone 
closely  conformed  to  the  curvature  of  the  wheel  on  the  lower 
descending  quadrant,  so  that  the  floats  will  partly  act  as  buckets, 
to  retain  the  water. 

With  a  low  fall  of  water,  a  long  breast  wheel  may  be  better 
than  an  overshot  of  diameter  equal  to  the  height  of  the  fall, 
since  its  longer  diameter  may  enable  it  to  retain  the  water 
longer. 

The  principal  horizontal  wheels  are  turbines.  They  work 
under  water  upon  a  vertical  axis. 

The  power  given  out  by  a  wheel,  other  things  being  the  same, 
depends  on  the  quantity  of  water  which  it  can  dispose  of.  Ac- 
cordingly, turbines,  being  small,  usually  revolve  with  a  very 


72  ELEMENTS   OF 

high  velocity,  while   the  ponderous   overshot  wheels  revolve 
slowly. 

Again,  for  practical  purposes,  turbines  may  be  distinguished 
as  cheap  and  empirical  ones,  arranged  according  to  partly  fanci- 
ful notions,  perhaps,  of  their  designers;  and  costly  highly 
finished  ones,  carefully  modelled  in  every  part  by  the  results  of 
the  soundest  theory  and  most  decisive  experiments.  Of  the 
latter  class,  in  this  country,  are  the  Jonval  Turbine,  in  the  form 
known  as  the  u  Collins  wheel,"  made  at  Norwich,  Conn.,  the 
Fourneyron  Turbine,  as  arranged  in  the  "  Boyden  wheel,"  and 
made  at  Lowell  and  Chicopee,  Mass.,  and  elsewhere,  and  the 
Swain  or  centre  discharge  wheel ;  also  made  near  Lowell.  All 
of  these  wheels  are  so  good  as  compared  with  many  empirical 
wheels  that  we  should  not  here  wish  to  discriminate  between 
them.  There  is  only  room  to  partially  illustrate  them ;  but  the 
main  difference  between  them  will  be  well  understood  by  ob- 
serving that,  in  the  "  Jonval,"  the  stationary  guides  are  above 
the  buckets,  the  bucket  face  is  a  warped  surface  whose  recti- 
linear elements  are  horizontal  and  radial,  and  the  water  is  dis- 
charged on  the  under  side  of  the  wheel  in  a  stream  of  the  radial 
width  of  the  bucket,  whereas,  in  the  "  Fourneyron,"  the  sta- 
tionary guides  are  within  the  revolving  part ;  the  buckets  are 
vertical  and  cylindrical,  with  their  rectilinear  elements  parallel 
to  the  axis  of  the  wheel,  and  the  water  is  discharged  horizontally 
at  the  periphery  of  the  wheel :  and,  finally,  in  the  "  Swain " 
wheel  the  guides  are  radially  exterior  to  the  buckets,  and  the 
water  is  discharged  underneath,  and  around  the  axis. 

There  are,  then,  briefly,  bottom  discharge,  lateral  discharge, 
and  centre  discharge  wheels ;  and  these  are  the  three  radically 
different  kinds. 

Description. — PL  XIV.,  Fig.  1,  is  a  vertical  section  of  the 
wheel,  and  Fig.  2  a  side  elevation,  showing  the  general  arrange- 
ment of  parts  very  nearly  as  in  the  proportions  of  a  two  and  a 
half  foot  wheel.  AA  is  a  section  of  the  wheel,  with  the  posi- 
tion of  the  top  and  bottom  edges  of  buckets.  It  is  keyed  to  the 
vertical  shaft  ST.  A' A'  are  developments  of  sections  of  buckets. 
BB  are  the  guides,  and  B'B'  developed  sections  of  them,  show- 
ing them  to  be  hollow  to  prevent  the  injurious  eddying  of  the 
water  which  might  occur  if  only  eo  were  the  wall  of  the  guide. 
CCC  is  the  gate,  which  consists  of  radial  bars,  CC,  as  long  as  the 
buckets  are  wide,  alternating  with  the  openings  C'C'.  The  gate 


MACHINE   CONSTRUCTION   AND   DRAWING.  73 

thus  is  essentially  a  circular  plate  perforated  next  to  the  circum- 
ference and  turning  around  the  shaft.  Such  a  gate  might  be 
thought  to  interfere  with  the  proper  flow  of  the  water,  but  the 
perpendicular  width  of  guide  opening  at  E.  is  so  much  less  than 
at  ee  that  half  of  ee  can  be  taken  for  a  gate  bar  without  inter- 
fering with  the  best  form  for  the  vein  of  water  flowing  through 
the  guides  of  the  wheel.  DD  is  the  lighter  plate  made  fast  to 
the  shaft.  By  receiving  a  part  of  the  upward  pressure  of  the 
water  confined  in  the  penstock,  F,  it  relieves  the  footstep,  E,  and 
bridge,  M,  from  a  part  of  the  weight  of  the  wheel.  The  foot- 
step, E,  is  of  lignum  vitse.  aa  is  a  loose  collar  around  the  shaft 
to  shut  out  water  from  the  interior  space  N'N'.  55  is  the  in- 
terior loose  gland  ring  for  the  same  purpose,  and  thus  the  two 
prevent  the  water  pressure  from  acting  on  the  wheel  centre,  or 
plate,  PQ.  This  plate  has  openings,  through  which  any  water 
which  may  leak  into  the  space  ~N'W  may  escape,  dd  is  the  loose 
gland  ring  for  the  lighter  plate,  to  prevent  water  from  escaping 
there.  The  exterior  loose  gland  ring,  cc,  is  the  one  in  which 
the  wheel  runs.  It  prevents  the  escape  of  the  water  from  the 
guides  and  wheel,  into  the  case  without. 

G  is  the  cast-iron  mouth-piece,  and  II  the  water  trunk,  through 
which,  and  the  penstock  or  chamber  F,  the  guides  B,  and  wheel 
A,  the  water  flows,  as  indicated  by  the  arrows.  But  observe 
that  as  the  buckets  A'  are  driven  by  the  water  rushing  through 
the  fixed  guides  B',  the  water  current  is  not  really  bent  as  indi- 
cated by  the  arrows  on  the  bucket  sections,  but  passes  straight 
on,  carrying  the  wheel  circumference  with  it,  as  indicated  ap- 
proximately by  the  lines  RE/.  J  is  the  upper  bearing  for  the 
wheel  shaft.  K  the  gate  shaft  for  turning  the  gate,  and  L  its 
packing  box.  NX  are  the  wheel  and  guide  cases,  and  the  whole 
is  supported  by  the  standards,  O,  in  the  bottom  of  the  wheel 
pit. 

Construction. — As  nearly  all  the  principal  parts  have  circular 
horizontal  sections,  a  plan  could  be  constructed  with  sufficient 
completeness  from  the  elevations. 

Where  so  many  thin  sectional  surfaces  occur,  it  would  be 
well  to  tint  them  instead  of  putting  in  so  many  short  section 
lines. 

A  detailed  view  of  the  buckets  is  given  on  PL  IY.,  Fig.  4 
This  figure  was  made  from  an  actual  bucket,  but  of  an 
abandoned  form.  The  great  rapidity  of  motion  of  the  wheel, 


74  ELEMENTS   OF 

and  of  the  water  flowing  through  it,  causes  the  form  of  the 
bucket  to  be  a  very  nice  matter,  so  that  we  would  not,  if  we 
could,  give  any  improperly  exact  information  concerning  it, 
which  had  been  obtained  by  long  and  costly  experiments.  The 
drafting  operations  of  laying  out  a  bucket  are,  however,  fully 
shown. 

The  face  of  the  bucket  of  a  Jonval  turbine  consists  of  two 
warped  surfaces,  meeting  in  a  common  element,  os,pq.  The  lower 
surface,  r's'p'q',  or  cdeg  —  c'd'e'g',  is  a  portion  of  a  right  heli- 
coid — the  same  as  the  screw  surface  of  a  square  threaded  screw 
— and  has  for  its  directrices,  the  central  helix,  CE — C'E',  and 
the  vertical  axis,  at  O,  of  the  wheel.  The  upper  surf ace,^XY, 
or  egha — e'g'h'a',  is  a  portion  of  a  conoid,  whose  directrices  are 
the  central  curve,  EA — E'A',  and  the  axis  of  the  wheel,  as  be- 
fore. The  elements,  as  rs  /  eg — e'g'  /  XY,  etc.,  of  both  of  these 
surfaces  are  horizontal,  when  the  wheel  is  in  position,  having 
the  horizontal  plane  for  their  plane  director.  Whence  we  have 
the  following  construction :  With  centre  O,  and  the  assigned 
radius,  =  r,  describe  an  arc,  CB,  of  the  plan  of  the  mid-line  of 
the  buckets,  and  wheel.  We  suppose  the  angles  DC"B"  =  m, 
and  DAF  =  n  (where  FA"  is  horizontal),  at  which  the  water  best 
enters  and  leaves  the  wheel,  to  be  determined  by  investigation. 
Also,  let  the  height,  A"B",  of  the  wheel  be  given.  The  de- 
veloped length,  C"B",  of  the  buckets,  may  then  be  found  thus  : 
C"G,  the  horizontal  distance  from  one  bucket  to  the 

^•xr 

next  =  — — j  where  n  =  the  number  of  buckets.  Draw  GE"  per- 
pendicular to  C"E",  and  produce  it.  Draw  E"A",  making 
QE"A"=m  +  "  .  Then  the  perpendicular,  DQ,  through 

the  middle  point  of  E"A",  will  meet  GE"  at  Q,  the  centre 
of  the  arc  E"A". 

Letra  =  25°,  though  it  may  be  less  than  20°,  let  n  =  100°, 
and  B"A"  =  8".  Having  assumed  C"E"  to  be  straight,  it  be- 
comes the  development  of  a  helix.  Therefore,  divide  it  equally 
at  pleasure,  project  its  divisions  on  C"B",  and  transfer  them, 
in  order,  to  CA  in  plan.  Through  the  points,  as  n,  thus  located 
on  CE,  draw  radii  from  O,  which  will  be  horizontal  projections 
of  elements,  limited  by  the  inner  and  outer  circumferences, 
OA  and  O«,  of  the  wheel.  Then  project  up  m  and  i  to  meet  a 
horizontal  line  from  m",  and  m'i'  will  be  the  vertical  projection 


MACHINE   CONSTRUCTION   AND   DRAWING.  75 

of  the  bucket  element  mi.  In  like  manner,  we  find  other 
points  of  the  front  and  back  curves  c'e'a'  and  d'g'h'  of  the 
bucket. 

A"E"  is  simply  a  circular  arc,  tangent  to  A"D"  at  A."  and 
to  C"E"  at  E",  and  hence  DE"  =  DA".  Having  drawn  the 
arc  A"E",  proceed  as  before  to  find  ea — e'a',  etc. 

The  flange  R'S'M'N'  is  for  the  purpose  of  fastening  the 
bucket  to  the  rim^,  PL  XIV.,  Fig.  1,  of  the  wheel,  while  the 
ear  afk'  stiffens  the  outer  comer  of  the  bucket. 


d — Double  Curved  Receivers. 

EXAMPLE  XXIY. 

The  Swain  Central  Discharge  Water-wheel. 

Description. — The  following  abridged  description  and  figures 
are,  by  permission,  from  a  paper  by  Hiram  F.  Mills,  C.  E.,  in 
the  Journal  of  the  Franldin  Institute  for  March,  1870 : — 

The  central  discharge  iron  wheel,  known  as  the  Swain  wheel, 
has  been  in  use  in  various  pails  of  New  England  for  several 
years,  and  has  been  justly  gaining  a  reputation  for  good  con- 
struction and  efficiency. 

Plate  XV.  represents  a  vertical  section  through  the  centre  of 
the  wheel  and  curb,  and  a  plan  of  one-quarter  of  the  buckets 
and  guides,  and  a  development  of  a  portion  of  the  outer  surface 
of  the  wheel. 

A  flume,  6  feet  wide  and  6  feet  deep,  leads  the  water  from 
a  canal  to  the  wheel.  It  enters  the  forebay,  6  feet  square  and 
19  feet  deep,  from  the  side  of  which  water  is  conveyed  to  the 
wheel. 

The  wheel-pit,  upon  the  floor  of  which  rest  the  cast-iron  sup- 
ports of  the  wheel  and  its  case,  is  14  feet  wide,  and  20  feet  6 
inches  long,  with  sides  5  feet  high. 

The  cast-iron  supply-pipe  and  the  quarter-turn,  D,  Fig.  1,  are 
4'98  feet  in  diameter  inside,  and  the  radius  of  the  central  line 
of  the  latter  is  3*75  feet.  The  former  is  T45  feet  in  length, 
and  is  firmly  bolted  to  the  side  of  the  forebay,  at  AB. 

The  quarter-turn  is  bolted  to  the  supply-pipe,  and  is  supported 


76  ELEMENTS   OF 

by  the  cast-iron  case,  C,  which  enlarges  to  have  an  internal  dia- 
meter of  6*98  feet.  This  case  extends  to  a  short  distance  below 
the  bottom  of  the  wheel,  and  is  supported  by  six  hollow  cast- 
iron  columns,  Y,  l-5  feet  long,  O8  feet  wide  radially,  and  0*3 
wide  tangentially,  and  presenting  acute  angles  to  the  escaping 
current. 

The  columns  also  support  the  cylindrical  disk  E,  which  sur- 
rounds the  lower  half  of  the  wheel,  and  upon  the  outside  of 
which  the  regulating-gate,  O,  slides;  and  by  means  of  three 
supports,  one  of  which  is  represented  at  F,  they  sustain  the 
annular  chamber  G,  also  the  disk  H,  which  cover  the  wheel, 
the  lower  shaft-coupling,  and  the  step ;  and  the  shaft-pipe,  I, 
which  extends  from  the  top  of  the  disk  through  the  upper  part 
of  the  quarter-turn. 

The  disk  K,  cast  with  the  six  supports  of  the  case,  sustains 
the  step  of  the  wheel  L,  and  the  main  shaft  M. 

The  step  L,  of  white  oak,  is  a  cylinder,  7  inches  in  diameter, 
terminated  at  top  and  bottom  by  cones,  and  having  an  extreme 
length  of  8  inches.  It  is  free  to  move  with  the  shaft-coupling, 
or  the  latter  may  move  upon  its  upper  surface. 

The  step  is  always  submerged,  and  to  maintain  its  surfaces  in 
as  good  a  condition  of  lubrication  as  possible,  several  vertical 
holes  are  bored  through  it,  and  filled  with  a  fine  quality  of 
plumbago. 

By  means  of  the  set-screws  K,  the  wheel  may  be  adjusted  to 
the  proper  height.  These  screws  are  reached  through  hand- 
holes  in  the  curved  disk  H,  which  connects  the  wheel  with  the 
shaft. 

The  regulating-gate,  OO,  is  represented  as  fully  open.  It 
consists  of  a  cylinder  of  cast-iron,  7-J-  inches  long,  3-51  feet  in 
diameter  inside,  having  at  the  bottom  a  narrow  flange,  against 
which  a  ring  of  leather  packing  is  held  by  means  of  bolts  and . 
a  cast-iron  ring,  by  which  leakage  under  its  lower  edge  is  pre- 
vented, and  at  the  top,  cast  with  it,  and  making  an  angle  of 
about  80°,  is  a  broad  flange  extending  outward  7J  inches,  with 
'an  edge  turning  downwards. 

This  flange  serves  as  the  lower  disk,  limiting  the  stream  of 
water  entering  the  wheel,  and  into  it,  projecting  vertically  from 
its  upper  surface,  the  guides  PP  are  cast. 

There  are  24:  guides,  21  of  which  are  straight  plates  of 
wrought-iron  ^  inch  thick,  and  10£  inches  long,  having  each 


MACHINE   CONSTRUCTION   AND   DRAWING.  77 

end  sharpened  to  a  thickness  of  ^  of  an  inch,  with  a  bevel  £ 
inch  long.  The  mean  distance  of  their  inner  edges  from  the 
centre  of  the  shaft  is  1-S35  feet,  and  they  are  distant  radially  one 
inch  from  the  outer  edge  of  the  buckets.  Their  direction  makes 
an  angle  of  22°,  with  the  tangents  through  their  inner  edges. 

The  remaining  three  guides  are  of  cast-iron,  of  the  form 
represented  in  plan  at  O  in  Fig.  2. 

Through  these  guides  pass  the  three  wrought-iron  rods,  ad- 
jacent to  the  supports,  F,  and  by  which  the  gate  is  raised  and 
lowered.  Two  of  these  are  represented  at  K.  They  extend 
from  the  under  side  of  the  gate  flange  through  stuffing-boxes  in 
the  upper  part  of  the  quarter-turn,  and  terminate  in  racks  SS, 
into  which  work  the  pinions  TT,  which  are  driven,  through  the 
action  of  the  worm  U,  by  a  crank. 

When  the  gate  is  raised,  by  which  movement  it  is  also  closed, 
all  of  the  guides  rise  through  slots  in  the  upper  disk,  which 
limits  the  stream  approaching  the  wheel,  and  which  is  similar 
in  form  to  the  lower  disk  already  described ;  and  are  enclosed 
in  the  guide-chamber  G.  By  this  arrangement  the  stream  pass- 
ing between  the  guides  is  decreased  in  height  in  proportion  to 
the  closing  of  the  gate. 

The  wheel,  W,  has  an  extreme  diameter  of  42  inches,  and  an 
extreme  height  of  15^  inches.  It  has  25  buckets  of  wrought- 
iron,  |-  of  an  inch  in  thickness,  which  are  formed  in  a  die,  and 
are  cast  into  the  upper  disk  aa,  which  forms  the  crown  of  the 
wheel,  and  into  the  band  &J,  which  surrounds  the  lower  part  of 
the  buckets  for  a  height  of  8 -42  inches,  leaving,  between  the 
top  of  this  ring  and  the  under  side  of  the  crown,  a  space  5 '35 
inches  high,  through  which  the  water  enters  the  wheel. 

The  horizontal  projection  of  the  buckets,  for  a  depth  of  5 
inches  from  the  top,  is  shown  by  the  heavy  lines  in  Fig.  2,  and 
Fig.  3  represents  the  development  of  a  portion  of  the  cylindrical 
surface  containing  the  outer  edges  of  the  buckets. 

The  diameter  of  the  cylinder,  which  would  contain  the  inner 
edges  of  the  buckets  for  a  depth  of  5  inches,  would  be  2'092 
feet.  Below  this  portion,  the  surface  which  would  contain  the 
inner  edges  of  the  buckets  is  generated  by  the  revolution,  about 
the  vertical  axis  of  the  wheel,  of  a  quadrant  whose  radius  is  8*4 
inches,  and  which  is  convex  towards  the  axis. 

The  under  side  of  the  crown  of  the  wheel  is  horizontal 
through  a  radial  distance  of  4  inches  from  the  outside.  For 


78  ELEMENTS   OF 

the  remaining  distance,  it  forms  part  of  a  surface  of  revolution, 
C,  whose  sections  through  the  axis  have  a  radius  of  11  inches, 
which  surface  continues  downward  and  towards  the  shaft,  and 
forms  part  of  the  cylindrical  socket  which  surrounds  the  step 
and  its  supports. 

The  following  dimensions  were  measured  after  the  wheel  was 
removed  from  the  pit. : — 

Vertical  distance  from  the  under  side  of  the  crown 

to  the  lower  edge  of  the  buckets 1  '148  feet. 

Vertical  distance  from  under  side  of  crown  to  top  of 

band 0-446  " 

Mean  shortest  distance  of  the  inner  edge  of  one 
bucket  from  the  adjacent  bucket  at  1  inch 

below  the  crown 0'065  " 

Ditto,  ditto  at  5  inches  below  the  crown O'OSO    " 

Ditto,  ditto  at  1  inch  from  the  outside  at  the  bottom.  0'135    " 

Mean  shortest  distance  from  the  inner  edge  of  one 

guide  to  the  adjacent  guide 0'214  " 

Mean  shortest  distance  from  the  outer  edge  of  one 

guide  to  the  adjacent  guide 0'332  " 

Mean  area  of  outlets  of  wheel 18'97  sq.  ins. 

Total  area  of  outlets  of  wheel 3'29  sq.  ft. 

From  a  series  of  ninety  careful  experiments,  the  interesting 
details  of  which  will  be  found  in  the  journal  referred  to,  it  was 
found  that  the  mean  maximum  efficiency  of  the  wheel  is  as  fol- 
lows, viz. : — 

With  full  gate,  81-^  per  cent,  of  the  power  of  the  water. 
With  three-quarters  gate,  77^  per  cent,  of  the  power  of  the 
water ;  and  with  one  half -gate,  69  T^-  per  cent,  of  the  power  of 
the  water. 

Construction. — Fig.  1  may  properly  be  made  on  a  scale  of 
three-f ourths  of  an  inch  or  a  whole  inch  to  the  foot ;  and  with 
the  sectional  surfaces  tinted,  instead  of  being  filled  with  shade 
lines. 


MACHINE   CONSTRUCTION   AND   DRAWING.  79 


CLASS  IIL-COMMUnCATORS. 

59.  These  are  pieces  whose  office  it  is  to  take  up  a  certain 
motion  at  one  point,  and  impart  it  unchanged,  or  modified  in 
velocity,  form,  direction,  or  uniformity,  at  another  point. 

Most  of  the  pieces  interposed  between  the  receiver  and  the 
operator  in  any  machine  are  but  a  succession  of  communica- 
tors, as,  for  example,  the  wheels  of  a  watch,  which  communicate 
the  motion  received  from  the  main  spring  by  the  barrel  to  the 
hands.  In  this  case,  the  original  velocity  is  greatly  changed. 
In  the  use  of  the  crank,  the  reciprocating  and  variable  velocity 
of  the  piston  of  a  steam  engine  is  changed  into  the  rotary  and 
uniform  motion  of  the  crank-pin  ;  and,  again,  toothed  wheels 
and  rocker  arms,  that  is,  arms  which  vibrate  about  a  fixed 
point,  change  the  direction  of  the  motion  received  by  them. 

A — Point  Communicators. 

Point  communicators  are  not  numerous.  Only  one  example 
is  given  here,  separately.  The  crank-pin,  and  the  cross-head, 
will  be  found  elsewhere,  as  parts  of  other  examples. 


EXAMPLE  XXY. 
Collins'  Shaft  Coupling. 

Description. — PL  XXX.,  Fig.  1,  is  a  sketch  merely  of  this 
coupling.  Shafts  are  necessarily  of  limited  length ;  though  a 
line  of  shafting  may  extend  the  whole  length  of  a  very  long 
room.  Some  of  the  requisites  of  a  good  coupling  are,  ease  of 
application,  permanence  of  adjustment,  lightness  of  separate 
parts,  and  neat  finish,  with  absence  of  projecting  parts.  These 
conditions  are  well  met  in  the  coupling  here  shown.  SS  is  one 
side  of  a  sleeve,  whose  two  halves,  together,  embrace  the  shaft. 
CR — C'B/  is  one  of  two  cone  rings  which  together  cover  the 
slightly  tapered  part,  ab,  of  the  sleeve  ;  rn — r'n'  is  one  of  the 


80  ELEMENTS   OF 

ring  nuts,  to  be  screwed  on  to  the  screwed  portions,  Sa,  SJ,  of 
the  sleeve,  by  inserting  a  pin  in  the  holes  r',  n' ,  etc.  It  thus 
drives  the  cone  rings,  whose  inner  bore  is  tapered  the  same  as 
ab,  upon  the  sleeve,  and  thus  clamps  the  two  parts  of  the  latter 
tightly  to  the  shaft.  Sometimes,  small  pins,  j},  inside  of  the 
sleeve,  enter  corresponding  holes,  one  in  each  piece  of  shafting, 
in  order  to  give  the  coupling  a  firmer  hold ;  but  this  is  not  ne 
cessary.  The  whole,  when  put  together,  is  a  smooth  cylinder 
capable  of  being  used  as  a  band  pulley  if  desired. 

Construction. — The  measurements  attached  to  the  sketch  al- 
low all  parts  to  be  accurately  drawn ;  with  an  exterior  view  of 
the  other  half  sleeve  ;  or  an  end  view  of  either  half. 


B — Line  Communicators. 

60.  Linear  communicators  are  distinguished  as  flexible  and 
rigid.  The  former  will,  for  convenience,  be  described  first ; 
on  account  of  the  connection  of  the  latter  with  subsequent 
forms  of  communicators. 


Cord,  and  Chain   Wheels. 

61.  The  motion  of  one  wheel,  or  of  a  curved  sector,  may  be 
communicated  to  another  by  means  of  a  band  or  belt,  a  cord, 
or  a  chain  passing  around  both  wheels ;  or  fastened  suitably  to 
a  point  on  the  circumference  of  each  sector.     In  either  case,  the 
wheel  and  the  band  are  both  of  so  simple  a  form  as  hardly  to  pre- 
sent any  fit  examples  for  graphical  construction ;  except  as  the 
curved   arms  often  seen  in  band  pulleys  may  afford  further 
practice  in  the  nice  construction  of  tangent  arcs ;  and  as  a  fully 
shaded  projection   of  two  or  more  band  wheels,  in  different 
planes,  might  make  an  effective  plate  of  shaded  drawing.     Such 
a  plate  the  student  could  readily  design  and  execute  for  him- 
self, after  having  learned  the  following  principles. 

The  present  subject  will,  therefore,  be  treated  only  in  relation 
to  the  leading  practical  principles  of  band  wheels  or  pulleys, 
belts  and  chains. 

62.  Angular  velocity  is  that   at  which   the   angular  space 
around  a  centre  is  swept  over  by  a  radius  turning  about  that 
centre. 


MACHINE   CONSTRUCTION   AND   DRAWING.  81 

For  purposes  of  comparison  it  is  estimated  at  a  unit's  dis- 
tance, as  a  foot,  from  the  centre.  Thus  if  a  point  on  the  pe- 
riphery of  a  wheel  of  4  ft.  radius  be  moving  at  the  rate  of  20 
ft.  per  second,  the  velocity  of  a  point  at  one  foot  from  the  cen- 
tre will  be  5  ft.  per  second,  and  this  will  be  the  angular  velocity 
of  the  wheel. 

63.  The  direction  of  the  motion  of  a  revolving  body  at  any 
point  is  estimated  on  the  tangent  at  that  point  to  the  circle  de- 
scribed by  that  point. 

The  direction  of  an  angular  velocity,  as  to  its  sense,  i.  e.,  as 
forward  or  backward,  right  or  left,  is  estimated  by  that  of  a 
watch  having  the  same  relative  position  to  the  observer  as  the 
given  motion.  The  hands  of  a  watch  are  said  to  move  from 
left  to  right,  since  they  really  do  so  in  passing  through  the 
upper  or  XII  point.  Any  opposite  rotary  motion  is  then  said 
to  be  from  right  to  left. 

THEOREM  I. 

A  rotary  motion  of  two  parallel  axes  may  be  maintained 
indefinitely,  and  in  one  and  the  same  direction,  for  both,  by  a 
band,  passing  directly  around  cylindrical  pulleys  in  the  same 
plane,  on  those  axes  /  but,  if  the  band  be  crossed,  the  rotations 
will  be  in  opposite  directions  ;  but  in  both  cases  tlw  ratio  of 
constant. 


FIG.  28. 


Let  A  and  B,  Fig.  22,  be  two  thin  cylinders  in  the  same 
plane,  secured  to  the  axes  A  and  B,  also  in  the  same  plane.    A 
leather  or  other  flexible  band,  abed,  whose  ends  are  united  to 
6 


ELEMENTS    OF 


make  one  piece,  may  then  be  passed  directly  and  tightly  around 
the  two  pulleys,  as  shown,  and  will  then  be  in  the  same  plane 
as  the  wheels.  Its  adhesion  to  the  wheels  will  then  be  sufficient 
to  communicate  the  motion  of  either  to  the  other.  And  as  no 
part  of  the  band  is  hindered  in  passing  any  point  touched  by  it 
on  the  wheel,  the  motion  in  either  elevation,  ab  or  ba,  may  be 
indefinitely  continued.  As  the  points  a  and  b  move  in  the 
same  direction  and  on  the  same  side  of  the  axes,  the  angular 
motions  of  the  wheels  will  be  in  the  same  direction.  But  if 
the  band  be  crossed,  as  in  Fig.  23,  the  points  a  and  b  being  on 
opposite  sides  of  the  plane  of  the  axes,  the  band  will  produce 
rotations  in  opposite  directions,  as  shown  by  the  arrows. 

Finally,  the  ratio  of  the  velocities  will  be  constant,  for  all 
points  of  the  band  must  move  with  equal  velocity,  else  it  would 
break ;  hence  the  peripheries  of  the  wheels  have  equal  velocities, 
which  are  equal  to  that  of  the  band.  Hence  as  each  wheel  has 
a  constant  radius,  its  angular  velocity  also  will  have  a  constant 
ratio  to  that  of  its  periphery,  that  is,  to  that  of  the  band. 
Hence  the  ratio  of  the  angular  velocities  to  each  other  will  be 
constant. 

Remark. — While  this  last  result  is  theoretically  true,  it  is 
not  so  practically,  if  there  be  any  slipping  of  the  band. 

THEOREM  II. 

A  band  should  be  crossed  by  giving  it  a 
half  twist,  in  a  plane  perpendicular  to 
that  of  the  wheels  which  hold  it ;  it  should 
be  shifted,  laterally,  by  operating  on  its 
advancing  side,  and  if  applied  to  a  cone 
wheel,  will  work  itself  towards  the  larger 
end  of  the  cone. 

First,  the  band  should  be  crossed  as  de- 
scribed ;  first,  to  bring  the  same  side,  and 
the  inner  side  of  the  leather  against  the 
pulley ;  and,  second,  to  make  it  cross  it- 
self flatwise,  as  at  D,  or  face  to  face,  in- 
stead of  edge  to  edge.  This  is  accom- 
plished by  taking  hold  of  the  band,  as 
shown  in  Fig.  24,  and  carrying  it  half 
round,  that  is,  with  a  half  twist,  as  indicated  by  the 


MACHINE    CONSTRUCTION   AND    DRAWING. 


arrow   C,   in   the    plane   OF,   parallel   to  the    plane   of    the 
axes. 

Second,  the  rigidity  of  the  band  in  the  direction  of  its 
width,  together  with  its  adhesion  to  the  surface  of  its  pulley, 
makes  any  point  of  it  follow  the  line  into  which  it  is  drawn 
at  any  point,  in  going  on  to  the  pulley  from  that  point. 


FIG.  26. 


Thus  a  band  A,  Fig.  25,  being  drawn  aside  by  a  looped 
rod  B,  just  before  striking  the  wheel,  will,  by  its  own  stiffness, 
follow  the  direction  aA.  till  it  touches  the  wheel,  and  will 
then  continue  in  that  direction. 

Hence,  in  all  shifting  of  bands  from  one  pulley  to  another, 
they  must  be  acted  upon  on  their  advancing  sides ;  and  any 
ordinary  lateral  action  applied  to  them  on  their  retreating 
side,  will  not  displace  them  on  or  from  their  pulleys. 

Third,  the  resistance  of  the  band  to  lateral  bending  likewise 
makes  it  work  towards  the  larger  end  of  a  conical  pulley. 
Thus  the  band  AB,  Fig.  26,  in  striving  to  fit  the  conical  pulley, 
C,  will  bend ;  and  .the  point  D  will,  by  the  resistance  of  the 
band  to  lateral  bending,  tend  to  move  in  the  line  D<#,  while,  by 
the  continuance  of  these  two  actions,  the  band  „  fi 
will  work  itself  to  the  larger  base  of  the  cone. 

Hence  the  simplest  method  of  keeping  bands 
upon  their  pulleys  is,  to  make  the  latter  consist 
of  two  conical  frusta,  with  a  common  larger 
base. 

Thus  band  pulleys,  even  when  running  with 
the  highest  velocities,  are  made  as  in  Fig.  27,  FIG.  27." 

slightly  coned  from  a  and  c  to  the  larger  central  diameter  at  ft. 
The  band  will  thus  keep  itself  upon  the  pulley,  without  either  ex- 


84 


ELEMENTS    OF 


ternal  guides  or  loops,  or  flanges,  all  of  which  would  wear  its 
edges  and  hinder  its  motion. 

The  principles  now  explained  enable  us  to  solve  the  following 
problem. 

PROBLEM   I. 

To  connect  wheels  lying  in  different  planes,  oy  a  band,  when 
the  intersection  of  their  planes  is  also  a  common  tangent  to  the 
two  wheels. 

This  general  problem  includes  several  cases  which  will  be 
taken  up  successively,  as  variations  from  a  given  case. 

I. — To  connect  the  wheels  so  that  they  shall  revolve  in  a  given 
manner.  The  band  should  be  led  on  to  each  wheel  in  the  plane 
of  that  wheel,  and  should  leave  each  wheel  at  the  point  of  con- 
tact of  the  common  tangent  to  the  two  wheels.  Let  PN  and 


FIG.  28.  FIG.  29. 

QN',  Fig.  28,  be  given  axes  not  in  the  same  plane,  the  direc- 
tions of  whose  axes  make  any  angle  with  each  other,  and  let  the 
motion  be  in  the  direction  of  the  arrows.  Let  CT  be  the  common 
tangent,  which  is  the  intersection  of  the  planes  of  rotation, 
BTC  and  ATC.  Then  the  band,  moving  as  shown,  must  enter 
the  lower  wheel  in  the  plane  BTC,  and  the  upper  one  in  the 
plane  ATC.  Also,  by  the  second  principle,  it  must  leave  the 
lower  wheel  at  C,  and  the  upper  one  at  T. 


MACHINE   CONSTRUCTION  AND  DRAWING.  85 

The  same  thing  is  shown  in  projection,  in  PL  XYL,  Figs.  6 
and  7,  where  the  same  letters  being  repeated  at  like  points,  the 
figures  explain  themselves,  by  the  help  of  the  arrows.  In  these 
and  the  following  figures,  the  horizontal  plane  of  projection  is 
taken  parallel  to  the  given  axes,  for  convenience  in  constructing 
the  projections  of  the  wheels. 

From  this  case  as  a  starting  point,  two  principal  variations 
may  be  made  :  first,  to  reverse  the  motion  of  either  one  of  the 
wheels  ;  second,  to  reverse  the  motion  of  both  of  them. 

II. — To  reverse  the  motion  of  either  one  of  the  wheels.  Let 
the  motion  of  the  upper  wheel  be  reversed  as  in  PI.  XYL,  Fig. 
8.  This  case  is  here  illustrated  with  the  directions  of  the  axes 
perpendicular  to  each  other.  Observing  the  points  of  analogy 
and  of  difference  between  Figs.  28  and  29,  it  appears  by  mere 
inspection  that,  to  reverse  the  motion  of  either  wheel  alone,  the 
common  tangent,  CT — C'T'.  to  the  two  circumferences,  which 
is  the  intersection  of  the  planes  of  rotation,  shifts  to  the 
opposite  side  of  the  wheel  whose  motion  is  reversed  ;  while  the 
other  wheel,  BC — B'C',  shifts  to  the  other  side  of  the  common 
normal,  N — N'jSP,  from  where  it  was  before. 

In  the  corresponding  change  from  PI.  XYL,  Fig.  7,  the  wheel 
BC  will  move  parallel  to  TA  till  its  point  C  shall  be  under  A. 
The  student  can  construct  the  figure.  If  BC — B'C"  in  this 
case  were  moved  on  its  own  axis,  parallel  to  itself,  it  would 
have  to  increase  in  diameter  in  order  to  preserve  a  common 
tangent  to  the  two  circumferences,  as  before.  But  in  this  case, 
the  velocity  ratio  between  the  axes  would  be  changed,  which 
might  be  undesirable.  Any  two  wheels,  whose  central  sections, 
AT  and  BC,  were,  as  seen  in  plan,  generated  by  any  one  point 
of  NO,  as  <z,  would  give  the  same  velocity  ratio. 
.  Fig.  29  illustrates  this  case  pictorially.  with  the  motion  of 
the  lower  wheel  reversed  ;  and  we  see,  as  before,  that  the  in- 
tersection, CT,  of  the  planes  of  rotation  is  tangent  on  the  op- 
posite side  of  tliat  wheel,  and  that  the  other  wheel,  Q,  is  on  the 
opposite  side  of  the  common  normal  from  what  it  was  before, 
in  Fig.  28. 

III. — To  reverse  the  motion  of  loth  wheels.  This  is  illus- 
trated in  PI.  XYL,  Fig.  9,  for  the  general  case  of  the  directions 
of  the  axes  making  any  angle  with  each  other.  Like  letters  for 


86  ELEMENTS    OF 

like  points  still  being  retained,  we  see,  by  comparing  with  PI. 
XYL,  Figs.  6  and  7,  that  each  wheel  goes  to  the  other  side  of 
the  common  normal,  X — X'X",  and  that  the  common  tangent, 
CT — C'T,  finds  its  contacts  on  the  opposite  side  of  each  wheel 
from  where  these  points  were  before. 

Let  a?=the  angle  between  the  directions  of  the  axes, 

A    and  B  the  radii  of  the  wheels  denoted  by  the 
same  letters,  and 

P  and  Q  their  respective  distances,  measured  on 
their  axes,  from  the  common  normal  X — N'N".  Then  it  is 
easily  found  that  for  wheel  A, 

P=B  cosec  x+ A  cot  x. 

and  for  wheel  B, 

Q=:A  cosec  #4-B  cot  x. 
which  when  a?=90°  reduces  to 

P=B;  and  Q  =  A;  or,  in  this  case,  the  distance 
of  each  wheel  (the  central  plane  of  its  width)  from  the  com- 
mon normal  equals  the  radius  of  the  other  wheel,  as  in  PI.  XVI., 
Figs.  6  and  8. 

The  twisting  of  the  band  at  its  departure  from  each  pulley  is 
undesirable,  and  the  more  so  the  nearer  the  wheels  are  to  each 
other.  We  therefore  next  show  how  to  avoid  this  evil  to  a 
great  degree. 

PROBLEM  II. 

To  connect  band  wheels  in  different  planes,  when  the  inter- 
section of  those  planes  is  not  a  common  tangent  to  the  wheels. 

Let  I— IT',  PL  XYL,  Fig.  10,  be  the  intersection  of  the  verti- 
cal planes,  QI  and  01,  in  which  are  the  wheels  TA — T'A',  and 
BC — B'C'.  Take  any  two  points,  mm'  and  nn',  on  I — I'l", 
and  from  mm' ,  draw  mA. — m'A.',  and  raB — m'B' ;  also  from 
nn' ',  draw  nT — n'T',  and  nC — n'C'.  Then  place  guide  pulley, 
pp' ,  in  the  plane  A'm'B',  and  another,  qq',  in  the  plane  TWO', 
and  a  band  led  around  the  four  wheels,  as  shown,  wrill  act  in 
either  direction,  as  indicated  by  the  opposing  arrows,  since  the 
band  enters  upon,  and  leaves  each  of  the  four  wheels  in  the 
plane  of  that  wheel. 

By  drawing  m'T'  and  n/A',  the  lines  to  B'C'  remaining  un- 
(jhanged,  and  placing  j?'  and  «/in  planes  B'm'T'  and  Cn'A',  the 


MACHINE   CONSTRUCTION   AND   DBA  WING.  87 

relative  direction  of  rotation  of  the  wheels  P  and  Q  would  have 
been  changed. 

The  student  can  now  design  an  arrangement  with  one  guide 
pulley  for  this  case,  giving  rotation  in  one  direction  only  ;  also 
an  arrangement  either  by  one  or  two  pulleys  for  giving  rotation 
in  either  direction  in  the  previous  cases. 

Notes  on  Band   Wheels. 

64.  The  foregoing  are  all  the  important  geometrical  principles 
connected  with  band  wheels.     Some  notes  are  added,  mostly 
from  an  extensive  recent  collection  on  the  subject.* 

Area. — 100  square  feet  of  belt  per  minute,  per  horse-power, 
at  a  belt  speed  of  about  1,800  feet  per  minute,  seems  to  be  a  fail- 
average  allowance  of  belting  to  power  transmitted,  according 
to  several  examples  from  various  authorities  and  from  actual 
practice. 

One  example  gives  only  24  sq.  feet  of  belt  per  horse-power 
per  minute,  at  a  speed  of  about  750  ft.  per  minute ;  and  another, 
68  sq.  ft.  per  horse-power  per  minute,  at  a  belt  speed  of  1,000  ft. 
per  minute ;  but  the  horse-power  transmitted  may  have  been 
variously  or  loosely  estimated. 

A  more  satisfactory  average  result  is  from  a  mean  of  twenty- 
seven  select  examples,  in  which  all  evidently  extreme  cases,  like 
that  of  24  sq.  feet  just  named,  had  been  rejected,  and  the  belt 
speed  disregarded,  as  the  various  particulars,  of  material,  arc  of 
pulley  embraced,  condition  and  tightness  of  the  belt,  might 
neutralize  or  outweigh  the  effect  of  difference  of  speed.  The 
mean  of  the  twenty-seven  examples,  then,  gives  about  76  sq.  ft.  of 
belt  per  minute  per  horse-power,  to  pass  a  given  point  on  the 
pulley. 

65.  Material. — Numerous  authorities  agree  that  oak-tanned 
leather  is  preferable  in  point  of  durability  to  all  other  substances 
for  belting  purposes.     These  other  substances  are  woven  rubber 
fabrics,  gutta-percha,  paper,  and  any  of  these,  or  like  materials 
with  metallic  strands  incorporated  into  them.     As  an  example  of 
a  very  large  belt,  there  may  be  mentioned  an  india-rubber  belt,  4 
ft.  wide,  320  ft.  long,  and  of  3,600  Ibs.  weight,  designed  for  a 
large  grain  elevator,  f 

*  See  "  Belting  Facts  and  Figures,"  in  the  Jour.  Fr.  Inst.     1868-70. 
t  J.  F.  Inst.     Sept.,  1869. 


88 


ELEMENTS   OF 


66.  Pulley  surface. — This  is  of  cast-iron  or  wood.     In  either 
case  the  power  transmitted  may  be  greatly  increased  by  cover- 
ing the  pulley  with  leather,  between  which  and  the  belt  the 
friction  will  be  very  much  greater  than  between  the  uncovered 
pulley  and  the  belt. 

67.  Belt  fastenings. — The  two  ends  of  a  belt  are  very  often 
fastened  by  lacing  with  leather  strings  through  two  sets  of 
holes,  thus  (Fig.  30)  :— 


Also  by  rivets,  and  by  "  'belt  hooks"  where  the 
ends  of  the  belts  are  hammered  on  to  the  thin 
plate,  armed  with  numerous  short,  sharp 
points,  which  go  through  the  belt,  and  can 
be  clinched  (Fig.  31). 

Thin  flexible  studs  are  also  used,  thus : — 


D— 


the  leather  being  only  slit  instead  of  punched,  so  as  to  save  loss 
of  resisting  section  of  the  belt. 

Each  variety  of  belting  material  may  have  its  appropriate  belt 
fastening.  But  ordinary  lacing,  like  Fig.  30,  is  by  many  con- 
sidered best  for  leather  belts,  and  always  sufficient  if  the  belt  is 
not  stretched  too  tightly.  The  belt  hook,  Fig.  31,  is  recom- 
mended for  rubber  and  paper  belts. 

68.  Side  against  the  pulley. — It  seems  to  be  agreed  on  all 
sides,  that  the  hair  or  grain  side  of  the  leather  should  be  against 
the  pulley,  and  for  two  reasons.  First :  that  side  is  smoother 
and  firmer,  and  therefore  adheres  more  closely  to,  or  has  a  better 
hold  upon,  the  face  of  the  pulley.  Second  :  because  the  strongest 


MACHETE   CONSTRUCTION   AND   DRAWING. 


69 


part  of  a  leather  belt  is  about  one-third  of  the  way  through 
from  the  flesh  side,  and  this  bears  the  tensile  strain  of  the  outer 
half  of  the  thickness  of  the  pulley,  while  it  is  also  freed  from 
abrasion  by  the  pulley. 

69.  Paper  belts. — These  are  a  new  invention  known  as  Graves' 
patent.     They  are  made  only  for  straight  and  unshifting  belts, 
not  less  than  five  inches  wide,  nor  to  embrace  pulleys  less  than 
six  inches  diameter,  and  are  particularly  recommended  for  heavy 
belts.     Examples  are  recorded  12  to  14  inches  wide,  and  from 
50  to  120  ft.  long. 

70.  Proper  tension. — Belts  should  by  no  means  be  strained 
to  anything  near  their  breaking  weight,  as  they  would  thus  be  so 
extended  as  to  be  too  loose  on  their  pulleys.     Leather  belts 
should  not  bear  a  strain  of  much  above  300  Ibs.  to  a  square  inch 
of  cross  section.     Gutta-percha  will  bear  about  400  Ibs.  to  a 
square  inch,  its  breaking  weight  being  about  1,680  Ibs.  per 
square  inch. 

71.  Effective  radius. — Where  nice  calculations  of  speed  are 
to  be  made,  and  where  the  belt  can  be  relied  upon  not  to  slip, 
the  effective  radius  of  a  pulley  is  estimated  to  the  middle  of  the 
thickness  of  the  belt,  the  particles  within  that  point  being  com- 
pressed, and  those  without  extended,  as  the  belt  bends  around  its 
pulley. 

72.  Dressing. — It  is  very  generally  recommended  that  the 
dressing  for  belts  should  not  consist  of  a  liquid  penetrating  oil, 
but  of  a  stiffer  composition,  such   as   one  of   tallow  and  oil, 
further  stiffened 

by  a  small  por- 
tion of  beeswax 
or  resin. 

73.  Driving 
power.  —  Al- 
though this  topic 
belongs  more  ap- 
propriately to  a 
treatise    on    the 

dynamics  of  machinery,  yet  an 
outline  of  the  elementary  consid- 
erations to  be  regarded,  seems  too 
interesting  to  be  omitted.  Let  E, 
Fig.  33,  be  an  experimental  fixed  pulley  on  a  fixed  axis,  and 


90 


ELEMENTS    OF 


thus  incapable  of  motion ;  and  let  T  and  t  be  weights  attached 
to  opposite  ends  of  the  same  belt.  K,  passing  over  the  pulley. 
Let  G  be  a  small  guide  pulley,  freely  turning  on  a  movable 
axis,  so  that,  as  it  is  made  to  press  the  belt  in  or  out,  more  or 
less  than  half  of  the  circumference  of  E  may  be  in  contact 
with  E.  Then  let  T  be  adjusted  to  each  different  length  of  arc 
of  E  in  contact  with  the  band,  until  it  be  sufficient  to  descend 
and  draw  up  t,  by  the  slipping  of  the  band. 

The  difference  between  T  and  t  will  vary,  first ^  with  the  co- 
efficient of  friction  for  the  material  of  the  belt  and  the  pulley ; 
second,  with  the  ratio  of  the  arc  of  contact  to  the  entire  circum- 
ference of  E,  and  with  the  width  of  the  band,  and  consequent 
absolute  values  of  T  and  t. 

The  ratio  of  T  and  t  will,  however,  depend  only  on  the  two 
first  particulars. 

From  a  table  of  values,*  found  experimentally,  as  just  de- 
scribed, the  following  examples  are  taken : — 


BELTS    IN    ORDIXABY   CONDITION. 
Q  =  T  -  t 


On  Cast-iron 
Pulleys. 

Unit  of 
Comparison 
=  t. 

Ratio  of  arc 
embraced, 
to  the  cir- 
cumference. 

T 

Q 

1.69 
2.41 
3.43 

.69 
1.41 
2.43 

1. 
1. 
1. 

0.3 
0.5 

0.7 

2575.3 
Rope 

2574.3 
s  on  rough 

1. 
tvoodeii  di 

2.5 
•tuns. 

Now,  for  the  case  of  pulleys  on  freely  revolving  axes,  see 
Fig.  34,  where,  to  produce  equilibrium,  a  weight,  Q  =  T  —  t, 
must  be  hung  from  a  second  pulley,  D,  on  the  shaft  AD,  and  of 
the  same  diameter  as  pulley  A.  If  A  —  B,  as  shown,  0.5  of  the 
circumference  of  each  will  be  embraced  by  the  belt,  and  we 
shall  have  from  the  table  the  relative  weights  of  t,  T,  and  Q 
marked  in  the  figure. 

*  Practical  Treatise  on  Mill-Gearing.     London :   Spon.     1869. 


MACHINE   CONSTRUCTION   AND   DRAWING.  91 

Next  replace  T  and  t  by  any  sufficient  motive  power,  applied 
at  C,  and  it  would  raise  the  weight  Q  at  a  uniform  speed  with- 
out slipping  the  belt. 

n  x  Q  may  in  like  manner  be  raised  by  treating  it  thus  : — 
nQ=nT— nt,  and  the  belt  must  then  be  made  n  times  as 
strong  as  before,  when  it  withstood  only  the  strain  T.  This 
can  be  done  by  making  it  n  times  as  wide  as  before.  If,  how- 
ever, it  be  made  n  times  as  thick-,  its  stiffness  may  interfere  with 
the  friction  of  an  equal  area  of  contact  being  increased  n  times, 
by  the  n  times  increased  strain  nT.  That  is,  the  ratio  of  T  and 
t  may  be  changed  so  as  to  make  nQ=rT — nt,  and  then  the 
strength  of  the  band  must  be  rT  times  as  great  as  before.  This 
could  be  determined  experimentally. 

74.  Relative  merits  of  belting  and  gearing.     Belting  is  much 
more  quiet,  and  more  readily  allows  a  change  of  relative  velo- 
city.    It  only  needs  to  be  properly  proportioned  and  applied,  to 
give  as  good  or  better  results,  according  to  eminent  practical 
authorities. 

A  belt  too  tightly  stretched  on  its  pulleys,  not  only  injures  it- 
self, but  produces  an  injurious  friction  of  its  pulleys  thus 
drawn  towards  each  other,  on  one  side  of  the  shaft  of  each.  It 
is  desirable,  therefore,  to  have  a  long  overhead  line  of  shafting 
run  through  the  centre  of  the  width  of  the  room,  so  that  belts 
can  pass  from  it  down  to  machines  on  opposite  sides  ;  and  thus, 
partly,  balance  the  opposite  pressures  upon  the  shaft. 

Rubber  or  paper  belts  may  be  used  for  uncrossed  and  un- 
shifted  belts,  and  when  running  in  the  open  air,  and  the  former 
also  in  damp  or  wet  places.  Leather  belts  may  be  used  in  other 
cases,  and  with  leather-covered  pulleys,  and,  if  of  abundant  width, 
will  run  quite  slack  without  slipping,  or  loss  of  power,  from  ex- 
cessive friction  by  undue  pressure  upon  the  axles. 

Transmission  by  Ropes,  Cords,  etc. 

75.  Hound  bands  of  leather  or  other  material  are  occasionally 
seen  on  a  small  scale,  driving  some  of  the  subordinate  parts  of 
a  machine,  or  as  a  substitute  for  belts  in  models,  etc.     They 
run  in  circumferences  variously  grooved  in  different  cases  to 
hold  them  in  place. 

Concave  sided  grooves,  forming  an  angle  at  the  bottom,  are 
recommended  in  place  of  Y-shaped  ones. 


92  ELEMENTS   OF 

Since  1850,  however,  the  transmission  of  power  ~by  wife 
ropes*  on  a  grand  scale,  has  often  been  adopted  in  Europe  as  a 
permanent  arrangement,  and  might  be  so  employed,  advanta- 
geously, wherever  the  source  of  power  and  the  place  of  its  appli- 
cation are  necessarily,  or  most  conveniently,  far  apart. 

One  of  the  most  prominent  cases  of  this  kind  is  that  of  a 
large  water  power  ia  a  spot  so  precipitous  as  to  afford  no  good 
building  site  near  it.  In  such  a  case,  the  great  expense  of 
building  in  a  bad  position,  or  of  constructing  a  canal  from 
the  water  power  to  the  distant  mill  driven  by  it,  may  be  avoid- 
ed by  the  use  of  wire  ropes  from  a  water  wheel,  placed  directly 
at  the  site  of  the  water  power. 

The  main  propositions  and  facts  concerning  this  topic  can  be 
briefly  expressed  in  a  few  sentences. 

The  use  of  a  round  endless  wire  rope,  running  at  a  great  velo- 
city in  a  grooved  sheave,  constitutes  the  transmission  of  power 
by  wire  rope. 

Thus,  the  power  of  a  100-horse  power  turbine  has  been  trans- 
mitted 3,200  feet  by  a  f-inch  wire  rope  running  on  13^  feet 
wheels,  making  114  revolutions  per  minute,  and  400  feet  apart. 

The  requisite  tension  is  obtained  by  the  weight  of  the  rope 
in  long  reaches,  where  the  deflection  of  the  rope,  at  rest,  will  be 
about  -£%  of  the  distance  between  the  wheels. 

Special  care  should  be  taken  to  set  each  wheel  squarely  on  its 
shaft,  and  the  latter  truly  perpendicular  to  the  line  of  trans- 
mission. 

When  the  wheels  are  at  different  heights,  a  smaller  arc  of  the 
lower  one  will  be  effectually  embraced  by  the  rope,  as  the  weight 
of  the  rope  then  makes  it  tend  to  drop  away  from  that  wheel. 
In  such  a  case,  the  rope  may  be  stretched  tighter  ;  or,  if  the  incli- 
nation of  the  line  from  one  wheel  to  the  other  be  great,  as  35° 
or  more,  guide  pulleys  level  with  the  upper  pulleys  should  be 
provided,  so  that  both  parts  of  the  rope  shall  be  first  vertical 
from  the  lower  to  the  guide  pulleys,  and  thence  horizontal  to 
the  upper  pulley. 

Chains. 

76.  Chains  of  various  forms  are  sometimes  used  in  place  of 
bands,  where  great  power  is  to  be  transmitted.  They  are  usu- 

*  Trans,  of  Power  by  Wire  Ropes.     Van  Nostrand,  N.  Y. ,  1869. 


MACHINE   CONSTRUCTION   AND   DRAWING.  93 

ally  made  either  with  toothed  links  to  engage  in  notches  on  the 
periphery  of  the  wheel,  or  in  carefully  riveted  square  links  to 
embrace  teeth  upon  the  wheel.  But  in  all  cases  the  arrange- 
ment is  expensive  and  troublesome,  being  liable  to  get  out  of 
adjustment  by  the  wear  of  the  rivets.  It  is  therefore  inferior 
to  toothed  gearing,  or  wire  rope,  for  long  transmissions. 

For  hoisting  purposes,  etc.,  where  the  motion  is  limited,  and 
the  chain  passes  around  only  one  barrel  or  drum  ;  if  the  latter 
be  suitably  grooved,  a  chain  of  common  oval  or  of  rectangular 
links  will  coil  itself  very  evenly  on  the  barrel. 


Ible  Linear  Communicators. 


77.  The  common  crank  may  be  seen,  in  its  double  form,  in 
the  cranked  axle  of  any  locomotive  with  inside  cylinders.     A 
single  crank  may  be  found  in  any  stationary  steam  engine  of 
the  usual  form,  having  a  cylinder  and  reciprocating  piston. 

Two  armed  cranks,  whose  arms  are  perpendicular',  or  oblique 
to  each  other,  go  by  the  general  name  of  bell-cranks,  being 
most  familiar  in  door-bell  connections.  They  also  enter  largely 
into  the  mechanism  of  organ-stops. 

78.  "Eockers,"PL  XVIL,  Fig.10,  s  and  A,  are  familiar  in  near- 
ly all  American  locomotives,  where  they  have  a  vertical  position 
on  each  side  of  the  engine,  and  communicate  the  motion  of  the 
outer  end  of  the  excentric  rods,  e,  to  the  valve  stems,  v.  A  rock- 
er or  "  rocker  arm,"  s,  vibrating  in  a  vertical  plane,  about  its 
lowest  point,  R,  as  a  centre,  may  be  called  a  standing  rocker  / 
one,  A,  which  similarly  vibrates  about  its  highest  point  as  a 
centre,  may  be  called  a  hanging  rocker.    The  valve  rod,  or  stem, 
-y,  of  a  locomotive  is  attached  to  the  upper  point  of  a  standing 
rocker,  and  the  excentric  rod,  0,  which  moves  it,  to  the  lower  end 
of  a  hanging  rocker  on  the  same  rocker  shaft,  R. 


EXAMPLE  XXVI. 

A  Locomotive  Parallel  and  Main  Connections. 

Description.— The  parallel  connection,  PI.  XVII.,  Figs.  1-2, 
is  the  heavy  bar  that  connects  the  driving  wheels  of  locomotives 
having  more  than  one  pair  of  drivers.  It  always  lies  parallel 


94  ELEMENTS    OF 

to  the  line  joining  the  centres  of  those  wheels.  Hence  its  name. 
The  bar  itself  is  a  very  simple  affair,  being  straight  and  of 
round,  or  nearly  rectangular,  or  sometimes,  I  section.  But, 
with  the  adjunct  parts,  forming  its  attachment  to  either  crank 
pin,  it  presents  some  useful  features  for  study  and  practice. 

E,  is  the  lighter  and  moulded  part  of  the  connecting  rod. 
The  square-cut  part,  at  each  end,  as  E  ss,  is  the  "  stub-end,"  and 
S  is  the  strap.  BB  are  the  boxes,  of  brass,  lined  with  "  Bab- 
bit" or  anti-friction  metal,  within  which  the  crank  pin,  P, 
works.  In  this  example,  the  front  face  of  each  box  is  formed 
with  a  moulded  cover,  best  understood  from  the  plan,  Fig.  2,  at 
BB,  also  shown  by  its  principal  circular  lines  in  Fig.  3,  which 
shows  a  plain  box  without  a  cover.  This  cover  shields  the  head, 
j9,  of  the  crank  pin.  As  each  half  of  the  box  wears  out  on  the 
inside,  it  is  set  up  against  the  crank  pin,  by  wedge  keys,  K  and 
&,  which  fit  into  vertical  square  cut  grooves  in  the  backs  of  the 
boxes  as  shown,  where  ss  and  tt  are  the  backs  of  the  boxes,  into 
which,  as  at  gg  in  the  plan,  the  vertical  edges  of  the  keys  set. 

The  rear  box,  being  slipped  into  the  strap  from  its  open  end, 
and  drawn  over  the  crank  pin,  the  front  box  can  then  be  like- 
wise slipped  in,  and  after  it  the  stub-end.  The  keys  can  then 
be  adjusted  till  the  box  is  close  to  the  pin, — the  edges  of  the 
vertical  joint,  M,  being  filed  away,  if  necessary,  to  secure  a 
proper  fit — while  also  the  bolt  holes  for  the  bolts,  II  and  T,  must 
agree  in  the  strap  and  stub-end.  These  bolts,  then,  hold  the 
whole  fast.  Their  nuts,  N,  and  jam-nuts,  n,  clamp  each  other 
to  the  bolt  threads,  and  bear  against  a  washer  iron,  "W.  The 
key,  K,  passes  through  W,  and  is  clamped  by  the  screw  bolt  e. 

The  similar  washer,  Y,  is  bolted  to  the  strap  by  F,  and  re- 
ceives the  key,  &,  which  is  clamped  by  e.  C  is  the  oil-cup. 

The  action  of  the  keys,  in  detail,  is  as  follows :  The  boxes 
having  become  loose  by  wear,  loosen  the  clamp-screws,  e,  and 
hammer  down  each  key  till  its  box  is  properly  tightened.  The 
tapering  edge  of  each  key  bears  against  the  unyielding  strap ; 
hence,  when  driven  in,  the  vertical  edges  move  towards  the 
crank  pin,  and  carry  the  boxes  along  with  them.  And  the  keys 
readily  descend,  since  the  slots,  as  ab  and  cd,  by  which  they  go 
through  the  strap,  are  wider  than  the  keys. 

Construction. — This  should  include  the  plan,  Fig.  2,  and  a 
detailed  view  of  a  box,  Fig.  3,  all  made  in  proper  relative 
position^  and  to  a  uniform  scale.  An  end  view,  or  a  section 


MACHINE   CONSTRUCTION   AND   DRAWING.  95 

through  hh,  may  be  substituted  for  the  plan.     The  scalo  may 
range  from  one-fourth  to  one-half  the  full  size. 

Similar  instructions  will  apply  to  the-  following  case : — 
The  JHciin  Connection-joint : — This,  Fig.  4,  which  is  merely  a 
sketch,  differs  from  the  parallel  rod-joint,  just  explained,  mainly 
in  being  heavier.  But  the  opportunity  is  here  improved  of  show- 
ing a  variation  in  the  construction,  such  as  is  frequently  seen. 
As  before,  R  is  a  part  of  the  main  connecting-rod,  from  the  for- 
ward driving-wheel  to  the  cross  head ;  E,  the  stub-end ;  B  and 
B,  the  boxes  around  the  crank- pin  Op.  SS  is  the  strap  and 
K  the  adjusting  key,  really  setting  into  the  front  box,  as  before. 
"With  one  key,  the  bolt-hole  for  the  bolt,  H,  is  slotted,  that  is, 
made  oblong  or  wider  than  the  diameter  of  the  bolt,  as  shown  by 
separate  dotted  lines  for  each.  Then,  when  this  bolt  is  loosened 
and  the  key  set  in,  it  first  sets  up  the  front  box,  and  afterwards 
acts  to  draw  on  the  strap  S,  and  thus  close  up  the  rear  box. 
Moreover,  the  key,  in  this  case,  is  a  screw-key,  passing  through 
the  stirrup  Ttf,  and  actuated  and  clamped  by  the  nut  and  jam, 
n  and  n. 

79.  Having  now  illustrated  the  principal  members  of  the 
main  train  of  a  locomotive — the  cylinder,  piston,  frame,  axle- 
box,  guides,  cross-head,  and  crank-pin  joints,  it  may  be  best  to 
sum  up  with  a  few  elementary  theorems  and  observations  about 
locomotive  action. 

80.  We  begin  with  the  following  principles.    First :  Action 
and  reaction  are  ever  equal  and  contrary.     Second  :   The  mo- 
ment of  a  force  is  its  product  into  the  lever-arm  with  which  it 
acts.     Third  :  The  point  of  contact,  R,  of  the  wheel  with  the 
rail,  Rr,  is  the  fulcrum  to  which  the  power  acting  at  the  crank- 
pin,  and  the  resistance  acting  at  the  axle,  are  referred.   Fourth  : 
Inertia  is  that  property  by  which  bodies  resist  either  an  acceler- 
ation or  retardation  of  velocity. 


THEOREM  III. 

The  effective  propelling  power  of  a  locomotive,  taken  at  the 
axle,  is  the  same,  whether  the  crankpm  is  above  or  below  the 
axle. 

Let  the  crank-pin  be  atjp,  Fig.  35 ;  let  the  engine  be  moving 


96 


forward ;  and  let  the  radius,  OR,  of  the  driving-wheel  be  3 
feet,  the  crank-arm  Op  —  Op'  =  1  foot,  and  the  pressure  on  the 
piston  9,000  pounds.  Then  a  force  of  9,000  pounds,  acting  as 
at  p,  4:  feet  from  R,  gives  a  moment  of  36,000,  which,  divided 
by  3,  the  lever- arm,  OR,  of  the  centre,  gives  12,000  pounds  as 
the  equivalent  force  acting,  as  at  Oa.  To  oppose  this,  there  is 
the  reaction  of  9,000  pounds,  against  the  back  cylinder-head,  com- 
municated through  the  engine-frame  and  body  to  the  front  axle- 
box,  and  represented  by  Ob.  This  leaves  a  surplus  of  3,000  pounds 
effective  pressure  forward,  at  O,  acting  to  propel  the  engine. 

On  the  other  hand,  let  the  crank-pin  be  at  p',  pressed  back- 
ward at  p'q'  with  a  force  pf  9,000  pounds,  acting  at  2  feet  from 
R.  The  moment  of  this  force  is  therefore  2  x  9,000  =  18,000, 
and  dividing  by  3  the  lever-arm  at  O,  we  find  6,000  pounds  as 
the  equivalent  force  acting  at  O  in  the  direction  of  Ob.  To 
oppose  this,  there  is  the  reaction  of  the  steam  pressure  of  9,000 
pounds  upon  the  front  cylinder-head,  and  thence  through  the 
frame,  etc.,  to  draw  the  latter  forward  against  the  axle.  This 
leaves  a  free  surplus  force,  as  before,  of  3,000  pounds  acting  at 
O  to  drive  the  engine  forward. 

It  follows  from  this  that  it  is  just  as  easy  to  start  a  load  with 
both  crank-pins  below  the  centre  O,  as  with  them  both  above. 


THEOREM   IY. 

The  pressure  between  the  axle  and  the  front  axle-box  of  an 
engine  going  forward,  is  double  that  between  the  axle  and  the 
back  axle-box. 


Fio.  35. 


We  have  seen,  Fig.  35,  that  there  is  a  tree  force  of  3,000 


MACHINE   CONSTRUCTION   AND   DRAWING.  97 

pounds  out  of  12,000  pounds,  acting  forward  at  O,  when  the 
crank-pin  is  at  p.  To  this  effective  force  is  opposed  the  sum  of 
all  the  train  resistances,  represented  by  the  additional  arrow  T)c. 
This  resistance  is  a  "  hanging-back,"  felt  through  the  frame  and 
drawing  the  front  axle-box  against  the  axle.  Thus  the  total 
pressure  between  the  front  axle-box  and  the  axle  is  12,000 
pounds.  Moreover,  this  result  is  constant  under  the  given  con- 
ditions ;  for  if  the  train  resistance  in  the  form  of  friction,  re- 
sistance of  the  air,  and  the  jerky  resistance  of  lifting  the  cars 
over  the  vertical  uiievenness  of  the  track  are  less  than  3,000 
pounds,  the  balance  will  be  made  up  by  opposing  forces  of 
inertia,  developed  in  increasing  the  speed,  until  the  former  re- 
sistances, alone,  equal  3,000  pounds ;  when  the  equilibrium  of 
uniform  motion  will  ensue. 

Again,  the  3,000  pounds  free  effective  pressure  forward  at  O, 
when  the  crank-pin  is  at^>',  is  opposed  by  the  train  resistances  as 
before,  which  act  to  draw  the  back  axle-box  from  the  axle. 
Hence  the  pressure  between  the  axle  and  the  back  box  is  6,000 
pounds,  or  one-half  as  much  as  there  is  between  the  axle  and  its 
front  box,  which  satisfies  the  enunciation. 

As  this  diminished  pressure,  and,  consequently,  diminished  axle- 
friction,  occurs  in  the  lower  half  of  the  crank-pin  circle,  it  follows 
that  if  there  is  any  sensible  advantage  in  starting  a  train  at  any 
time,  it  is  when  both  cranks  are  below  the  axle,  though  this 
happens  to  be  just  opposite  to  the  notion  said  to  be  held  by 
some  engine-drivers. 

THEOREM  Y. 

The  piston,  etc.,  move  in  space  faster  than  the  engine,  going 
forward,  in  the  forward  stroke,  and  slower  in  the  backward 
strolte. 

The  piston,  piston-rod,  and  cross-head  all  move  together,  and 
in  the  same  direction.  Let  the  motion  of  the  piston,  therefore, 
represent  them  all. 

Now  the  piston  of  a  locomotive  has  a  compound  motion.  1st, 
its  general  motion  forward,  in  common  with  all  points  of  the 
engine.  %d,  its  own  proper  motion  relative  to  the  cylinder, 
which  is  the  same  as  it  would  have  in  a  stationary  engine  having 
an  equal  cylinder,  and  working  with  the  same  rapidity.  The 
joint  effect  is,  that  in  its  forward  stroke  the  piston  is  moving 
7 


98  ELEMENTS    OF 

forward  in  space,  or  relative  to  any  fixed  object,  faster  than  the 
engine;  but,  in  its  backward  stroke,  slower  than  the  engine. 
Thus  a  piston  of  two  feet  stroke,  making  three  double  strokes 
per  second,  moves  in  its  cylinder  at  the  rate  of  twelve  feet  per 
second.  Acting  on  a  seven-foot  driving  wheel,  the  three  cor- 
responding revolutions  of  the  latter  would  carry  the  engine 
forward  very  nearly  sixty-six  feet  per  second,  which,  by  the 
way,  is  forty-five  miles  per  hour.  Then,  during  the  forward 
stroke,  supposing,  for  convenience,  that  the  piston's  proper  mo- 
tion is  uniform  at  all  points  of  the  stroke,  though  it  really  is 
not  so,  it  will  move  forward  in  space  at  the  rate  of  seventy- 
eight  feet  per  second ;  but  in  its  backward  stroke  it  will  move 
forward  relative  to  the  ground  with  a  velocity  of  fifty-four 
feet  per  second. 

And  the  above  example  fairly  represents  all  actual  cases,  and 
thus  the  theorem  is  proved. 

THEOREM  VI. 

The  crank-pin  has  an  accelerated  motion  in  space,  from  ^ts 
lowest  to  its  highest  point,  and  a  retarded  one  from  its  highest 
to  its  lowest  point.  Also,  it  moves  faster  than  the  engine  dur- 
ing the  forward  stroke  of  the  piston,  and  slower  during  the 
backward  stroke,  the  engine  having  a  forward  motion. 

To  demonstrate  this  theorem,  refer  to  PI.  IX.,  Fig.  2,  where 
AP  is  the  rail,  AQ  the  initial,  A'G  the  middle,  and  PQ'  the 
final  position  of  the  driving-wheel  for  one  revolution.  AGP  is 
then  the  cycloid  described  in  space  by  the  point  A  of  the  cir- 
cumference of  the  wheel ;  and  agp  is  the  prolate  cycloid  de- 
scribed by  the  crank-pin  in  making  a  complete  revolution  from 
its  lowest  point.  The  cycloid  may  be  constructed  as  in  Prob. 
III.  The  prolate  cycloid,  agp,  is  also  found  in  a  very  similar 
manner.  Thus,  when  the  diameter,  M'F',  becomes  vertical  at 
m,  g  will  be  aty,  as  far  to  the  left  of  the  vertical  line  at  in  as  g 
now  is  to  the  left  of  a  vertical  aty".  Or,  what  amounts  to  the 
same  thing,  fo  =f"n,  and  the  like  is  true  for  e,  d,  etc.  Thus 
the  distance  of  d  from  A'G  equals  that  from  d"  to  the  vertical 
at  Jc,  which  is  the  vertical  position  of  the  diameter  K'D'. 

This  being  understood,  observe  that  the  horizontal  spaces,  a'V, 
b'c',  etc.,  corresponding  to  the  equal  angular  motions  g"m", 
m"l",  etc.,  of  the  crank-pin,  increase  from  a  to  g,  that  is,  from 


MACHINE   CONSTRUCTION   ANT)   DRAWING.  99 

the  lowest  to  the  highest  point  of  its  path.  But  these  equal 
angular  spaces  indicate  the  uniform  advance  of  the  engine. 
Therefore  the  crank-pin  motion  is  accelerated,  as  described. 
And  as  the  remaining  half,  gp,  of  its  path  is  equal  to  ag,  its 
motion  is  retarded  as  described. 

Again,  dk'  is  the  horizontal  measure  of  the  space  described 
by  the  crank-pin  during  the  forward  stroke  of  the  piston,  cor- 
responding to  the  semicircle,  rqD,  of  the  crank  circle ;  while 
He"  is  the  corresponding  forward  motion  of  the  engine,  since  k 
and  If''  mark  the  two  vertical  positions  of  the  horizontal  diame- 
ter K'D'.  But,  making  a'd'"  =  a'd',  we  have  d'"ad'  for  the 
path  of  the  crank-pin  during  a  backward  stroke  of  the  piston, 
and  d'"d'  for  its  corresponding  horizontal  motion,  which  is  less 
than  kk".  Hence  the  relative  velocities  of  the  crank-pin  and 
the  engine  in  the  two  piston-strokes  are  as  enunciated. 

THEOREM  VII. 

The  wear  of  the  two  cranJc-pin  boxes  is  equal. 

This  result  follows  from  the  equal  pressures  on  the  crank-pin 
in  the  upper  and  lower  half  of  its.  circular  path,  as  found  in  the 
last  two  theorems.  In  the  upper  semicircle,  the  pin  being 
drawn  forward  by  the  piston,  etc.,  the  back  box  is  drawn  against 
the  crank-pin ;  while,  in  the  lower  semicircle,  the  pin  is  pushed 
by  the  connecting-rod,  the  front  box  is  pressed  against  it,  but 
with  the  same  pressure — of  9,000  pounds,  in  the  last  example 
supposed — as  before. 

But  as  the  difference  of  taper  of  the  keys,  PI.  X\rIL,  Fig.  1, 
K  and  &,  seems  to  indicate  an  opinion  that  the  front  box  wears 
faster,  since  its  more  rapidly  tapering  key  would  set  it  up  faster, 
the  question  may  be  more  fully  examined. 

When  the  crank-pin  has  a  retarded  motion,  the  inertia  of  the 
connecting-rod,  etc.,  resists  this  diminution  of  speed  by  striving 
to  go  on  uniformly,  and  it  thus  increases  the  pressure  between 
the  hacJt  crank-pin  box  and  the  pin.  But  the  crank-pin  also 
resists  an  acceleration  of  its  motion,  and  thus  presses  back  the 
front  box  against  the  pin. 

Let  us  now  examine  the  results  for  both  strokes. 

From  d"  to  g",  corresponding  to  d"fa  in  space,  PI.  IX.,  Fig. 
2,  the  steam  pressure  of  the  front  box  against  the  crank-pin  is 
diminished  by  that  of  the  lacJc  box,  caused  by  the  resistance  of 


100  ELEMENTS   OF 

the  connecting-rod,  etc.,  to  retardation  •  and  from  g"  to  s",  cor- 
responding to  ad  in  space,  the  same  steam  pressure  is  increased 
by  that  of  the  front  box,  caused  by  the  resistance  of  the  same 
parts  as  before,  to  acceleration. 

On  the  other  hand,  from  s  to  g,  corresponding  to  dg  in  space, 
the  steam  pull  of  the  ~back  box  against  the  crank-pin  is  dimin- 
ished by  the  continual  resistance  through  the  front  box  to  accel- 
eration of  the  connecting-rod,  etc. ;  while  from  g  to  d",  cor- 
responding to  gk'  in  space,  the  same  pull  is  increased  by  the 
resistance,  through  the  back  box,  to  retardation  of  the  connect- 
ing-rod, etc. 

Thus,  as  the  curve  agp  is  symmetrical  with  respect  to  AG, 
the  pressure  of  the  crank-pin  boxes  against  the  crank-pin  are 
equal  during  the  forward  stroke,  corresponding  to  sgd"  or  dgk', 
for  the  l>ack  box ;  and,  during  the  backward  stroke,  correspond- 
ing to  d"g"s  or  d'"ad'  for  tln.e  front  box. 

Hence  we  conclude  that  the  difference  of  taper  of  the  keys  K 
and  &,  PI.  XVIL,  Fig.  2,  is  arbitrary,  or  only  because  there  was 
not  room  for  so  large  a  key  as  K  behind  the  crank-pin. 

80.  A  few  fundamental  principles  concerning  the  mutual  re- 
lations of  boiler,  cylinder,  driving-wheel,  speed,  and  load,  being 
doubtless  of  interest  to  students,  the  following  is  here  added  : — 

It  must  be  premised  that  locomotive  power  does  not  reside 
primarily  in  a  large  driving-wheel,  or  steam-cylinder,  but  in  the 
boiler  capacity  to  deliver  steam  of  given  pressure,  at  a  certain  rate. 
This,  again,  depends  on  the  proportion  and  position  of  the  fire- 
box and  flues  relative  to  the  water  spaces  of  the  boiler ;  and,  last, 
without  going  back  of  causes  acting  in  the  engine,  to  the  primeval 
sunshine  as  the  power  which  produced  the  vegetable  growths 
from  which  coal  came ;  the  power  in  question  resides  ultimate- 
ly in  the  coal  consumed  by  the  engine. 

Let  the  duly  related  fire  and  water  spaces,  taken  together,  be 
regarded  as  the  given  boiler  capacity  for  steam  delivery  at  a 
given  pressure  and  rate,  and  we  shall  have  the  following  theo- 
rem. In  it  the  further  mechanical  principle  is  employed,  that 
the  work  of  a  force  is  the  product  of  its  intensity,  or  the  pres- 
sure it  can  produce,  by  the  space  through  which  it  acts. 

THEOREM  VIII. 
With  a,  gi/oen  toiler  capacity  and  size  of  cylinder -,  the  larger 


MACHINE    CONSTRUCTION   AND   DRAWING.  101 

the,  driving-wheel,  the  greater  the  adaptation  to  a  light  load  at 
a  high  speed  /  and,  conversely,  the  wheel  l>eing  given,  the  larger 
the  cylinder  the  greater  the  adaptation  to  the  'moving  of  a  large 
load  at  a  low  speed. 

This  theorem  can  be  better  established  by  a  numerical  exam- 
ple than  by  abstract  reasoning.  Then  let  the  following  suffice. 

Suppose  a  boiler  capable  of  supplying  20  cubic  feet  per  second 
of  steam,  at  a  mean  pressure  of  100  pounds  per  square  inch,  in 
the  cylinder,  and  that  each  cylinder  has  a  capacity  of  2  cubic 
feet.  Then  5  double  strokes,  or  10  single  strokes,  per  second  for 
each  cylinder,  with  the  steam  cut  off  at  half  stroke,  will  consume 
10  cubic  feet  of  steam  for  each  cylinder,  or  20  feet  for 
both.  Next,  suppose  the  driving-wheels  to  be  7  feet  in  diame- 
ter ;  then  the  circumference  of  each  will  be  about  22  feet,  and 
the  five  double  strokes  will  advance  the  engine  110  feet.  Let 
the  piston  have  an  area  of  150  square  inches,  then  the  stroke 
will  be  the  volume  of  the  cylinder  divided  by  150  = 

3456  cub.  ins.      no  .     , 

— : =  23  inches,  very  nearly. 

150  sq.  ins. 

Then  the  10  single  strokes  of  each  piston  =  230  inches  = 
19.2  feet  very  nearly,  which  is  the  space  passed  over  by  the 
piston  under  the  steam  pressure  of  150  x  100  =  15,000  pounds. 
Now,  if  the  train  have  a  uniform  velocity,  the  work  of  the  steam 
will  be  in  equilibrium  with  that  of  the  resistances,  and  we  have, 
considering  the  two  cylinders, 

2  x  15,000  x  19.2  =  x  x  110  ft., 

2  x  15,000  x  19.2       K00 
whence  x  =  —     — ^) —        ~  =  5236.  -f ,  pounds ....  (1) 

as  the  sum  of  all  the  resistances.  A  velocity  of  110  feet  per 
second  =  that  of  a  mile  in  48  sec.,  or  -f-  of  a  minute,  =  75  miles 
per  hour.  Now,  suppose  the  resistance  of  the  atmosphere  at  30 
miles  an  hour  to  be  equal  to  all  the  other  resistances  on  a  level, 
and  to  increase  as  the  square  of  the  velocity ;  and  let  10  pounds 
to  the  ton  be  the  force  required  to  overcome  these  other  resist- 
ances on  a  level.  Now  75  =  «  °f  30  and  (o)  =  "T* 

Then  let  y  =  total  train  resistance,  other  than  from  the  at- 
mosphere, here  assumed  to  be  uniform, 
or,  y  =  atmospheric  resistance  at  30  miles  per  hour,  and 

—r-  =  atmospheric  resistance  at  75  miles  per  hour. 


102  ELEMENTS   OF 

Hence,  -~-  -f  y  =  ~  y  =  total  train  resistance  of  all  kinds 

=  5326  pounds, 
whence  y  =  —    9  X—  =  722.2  pounds. 

Now,  at  10  pounds  per  ton  of  power,  this  force  would  move 

7222 

'    =  72.22  tons  on  a  level.   Allowing  30  tons  for  the  weight 

of  the  engine,  the  balance  of  42.22  tons  would  be  equal  to  about 
two  heavy  and  well-filled  passenger  cars ;  a  very  light  load  evi- 
dently for  such  an  engine,  at  ordinary  speed. 

These  results  are,  of  course,  not  given  as  perfectly  accordant 
with  facts.  Train  resistances,  including  those  peculiar  to  the 
engine,  other  than  atmospheric,  are  nbf;  really  uniform  at  all 
speeds ;  the  total  atmospheric  resistance  depends  partly  on  the 
number  of  cars,  and  on  their  distance  apart ;  and,  finally,  there 
are  little  or  no  definite  and  understood  results  of  experiment 
with  very  high  speeds.  Still,  the  above  example  sufficiently 
verifies  the  theorem. 

Without  going  through  the  other  cases  in  a  similarly  detailed 
manner,  it  is  sufficiently  evident  that  if  the  driving-wheel  be 
reduced  to  four  feet,  the  only  result  would  be  to  increase  the 
load  and  decrease  the  speed.  For  the  number  of  piston  strokes 
must  be  unchanged,  else  steam  would  either  waste  at  the  safety- 
valve,  or  fail  to  supply  the  cylinder  at  the  required  pressure. 
A  four-foot  wheel  will  advance  the  engine  about  12.6  feet  at 
each  revolution,  or  63  feet  for  the  5  double  strokes  of  the  piston  ; 
and  as  the  work  of  the  steam  in  the  cylinder  is  unchanged,  that 
of  the  resistance  will  be  so  also,  and  for  the  diminished  space 
through  which  the  resistance  is  felt  during  these  five  double 
strokes  we  shall  have  in  place  of  (Eq.  1)  : 

2  x  15,000  x  19.2 
so  =  -     — £5 —          -  =  9142.8  pounds, 

to  be  spent  on  the  train,  and  atmospheric  resistances,  from  which, 
by  a  similar  calculation  to  the  previous  one,  and  remembering  that 
63  feet  per  second  —  about  43  miles  per  hour,  we  find,  after  de- 
ducting the  engine  as  before,  a  load  approximately  of  16  care  at 
18  tons  each,  loaded. 

Finally,  with  the  driving-wheel  of  fixed  size,  and  the  cylinder 
variable,  let  us  again  take  a  four-foot  driving-wheel,  and  let  the 


MACHINE    CONSTRUCTION   AND   DRAWING.  103 

cylinders  be  of  4  cubic  feet  capacity  each,  or  of  about  19  inches 
diameter  and  24  inches  stroke.  The  capacity  being  thus  doubled, 
the  number  of  strokes  necessary  to  consume  the  given  volume 
of  steam  at  the  given  pressure  will  be  halved,  giving  2|  double 
strokes  per  second,  =  10  feet  per  second  piston  speed,  which 
will  advance  the  engine  31.5  feet. 

The  piston  area  of  each  cylinder  =  288  square  inches,  whence 

in  place  of  (Eq.  1)  we  should  have  x  =  2x28>S°0xl°  =  18,286 

ol.o 
pounds. 

Also  31.5  feet  per  second  =  about  20  miles  per  hour.  Hence 
the  given  suppositions  about  atmospheric  resistance  would  now 
give 

y  x  %y  =  18,286 

or  y  =  12,660  very  nearly,  which  at  10  pounds  per  ton,  to 
overcome  other  than  atmospheric  resistances, 
gives  a  load  of 

1,266  tons,  or,  deducting  36  tons  for  engine, 
leaves  1,230  tons  of  load,  or 

70  cars  at  about  17  tons  each,  including  their 

load. 

None  of  these  results  may  correspond  very  nearly  with  prac- 
tice, though  they  may  usefully  indicate  the  path  of  calculation 
and  experiment  to  be  followed  in  actual  cases. 

These  principles  concerning  the  adaptation  of  engines,  of 
certain  design,  to  a  certain  load  and  speed,  do  not  imply  that  an 
engine  of  different  design,  but  with  the  same  boiler  capacity, 
cannot  handle  the  same  load  at  the  same  speed.  For  if,  as  we 
reduce  the  driving  wheel,  the  cylinder  be  also  reduced,  so  as 
to  consume  the  same  quantity  of  steam  at  the  same  pressure  as 
before,  by  means  of  the  more  numerous  strokes  which  a  smaller 
wheel  would  require  to  maintain  the  given  speed  of  the  train, 
the  work  of  the  steam  in  the  cylinder  will  be  the  same  in.  both 
cases,  and  this  work  may  thus  be  expended  in  producing  the 
required  high  speed  of  a  small  load.  Accordingly,  within  the 
past  ten  years  there  has  been  a  very  general  reduction  of  the 
driving  wheels,  from  6£,  and  6  ft.,  diameter,  to  5£,  and  5  ft.,  the 
cylinder  remaining  the  same,  instead  of  an  enlargement  of  the 
cylinder,  in  order  to  move  the  heavier  trains  of  later  years 
at  an  undiminished  speed.  In  either  case,  however,  either  an 


104  ELEMENTS   OF 

enlargement,  or  an  improved  proportioning,  of  the  boiler, 
would  be  required  to  provide  the  increased  quantity  of  steam 
demanded. 

Some  of  the  advantages  of  small  cylinders  and  drivers  are, 
reduced  height,  and  consequent  increased  steadiness  upon  the 
track,  greater  lightness  of  running  parts,  and  increased  facility 
of  handling  them  in  the  shop.  And,  by  an  elegant  analogy,  as 
the  human  frame,  the  most  inimitable  of  all  machines,  per- 
forms better  with  full,  muscular  body,  and  finely  moulded  limbs, 
so  we  may  expect  that  improved  locomotive  action  is  to  be  next 
sought  in  steel  boilers,  safely  carrying  200  Ibs.,  or  more,  per 
square  inch,  of  steam  pressure. 


EXAMPLE  XXYII. 
A  Working- Beam. 

Description. — Engines  may  be  divided,  in  regard  to  the  rela- 
tive position  of  the  cylinder  and  shaft,  into  those  in  which  the 
axes  of  the  cylinder  and  of  the  main  shaft  are  in  the  same 
plane,  and  those  in  which  they  are  not  in  the  same  plane.  The 
ordinary  horizontal  engines  and  vertical  engines  are  of  the 
former  kind.  In  these,  PL  XVI.,  Fig.  4,  the  crank.  OC,  con- 
necting rod,  CII,  and  piston  rod,  PH,  are  all  in  one  and  the 
same  horizontal  or  vertical  line  together  at  two  positions  of  the 
crank.  In  the  other  class,  the  shaft,  O,  PI.  XVI.,  Fig.  5,  is  at 
right  angles  to  the  direction  of  the  piston  rod,  LP,  and  the  con- 
necting rod  and  piston  rod  are  parallel  in  the  two  vertical  posi- 
tions of  the  crank,  OR.  In  this  case  the  piston  rod  communi- 
cates its  motion  to  the  connecting  rod  through  a  working-beam, 
WB,  oscillating  on  a  fixed  centre,  C. 

PI.  XVI.,  Figs.  1,  2,  represents,  with  a  trifling  alteration  of 
some  of  the  mouldings,  which  it  would  be  quite  tedious  to  draw 
on  a  small  scale,  the  beam  of  the  Brooklyn  Water-Works 
Pumping  Engine  Xo.  2.  Its  ponderous  character  may  be  seen 
from  its  main  measurements,  about  31  ft.  8  in.  extreme  length, 
7  ft.  4  in.  extreme  width,  and  a  thickness  varying  from  6  in.  in 
the  web  to  2  ft.  4  in.  at  the  hub. 

The  hub  is  chambered  out,  at  gh,  to  avoid  so  great  an  extent 
of  turned  bearing  as  would  otherwise  have  to  be  made.  CO — C' 


MACHINE   CONSTRUCTION   AND   DRAWING.  105 

is  the  main  centre ;  DD'  is  the  point  of  attachment  of  the  con- 
necting rod,  or  of  the  liak,  as  BL,  Fig.  5,  to  the  piston  rod ;  W 
is  the  point  of  attachment  of  a  pump  rod. 

This  beam  is  not  of  particularly  fine  outline,  being  bounded 
by  circular  arcs.  A  more  elegant  form  would  be  given  by  a 
parabolic  outline  as  sketched  in  Fig.  3,  where,  if  too  clumsy 
when  d  is  made  the  end  of  the  beam,  and  abed  is  bounding  curve, 
the  latter  can  be  prolonged,  as  in  the  curve  ce,  making  d,  the 
vertex  of  the  parabola,  the  centre  of  the  pin. 

Indeed,  by  merely  proportioning  the  thickness  of  the  beam 
properly  for  strength,  any  other  similarly  curved  outline  may  be 
taken  for  its  elevation,  as  a  single  circular  arc,  or  an  ellipse, 
for  each  long  side  AG  or  A'F. 

The  great  weight  of  each  half  of  the  beam  itself,  acting  at  its 
centre  of  gravity  and  supported  at  C,  acts  to  separate  the  par- 
ticles of  iron  at  A'  and  to  compress  them  at  A.  To  resist  this 
tendency,  the  lower  flange,  AjA",  is  made  vertically  thicker,  as 
shown  at  those  letters. 

Construction. — Let  the  exercise  be  varied  by  adopting  some 
of  the  outlines  just  mentioned.  The  plan  will  be  a  sufficient 
guide  for  showing  the  mouldings,  as  mn}  and  the  end  of  the 
beam,  in  the  section. 


EXAMPLE  XXYIII. 
A  Stephenson  Link. 

Description. — There  is  some  difficulty  in  either  clearly  ex- 
plaining the  separate  members  of  the  train  of  parts  which  com- 
pose a  locomotive  valve  motion  before  explaining  the  whole,  or 
in  explaining  the  whole  concisely,  before  describing  its  several 
parts. 

In  adopting  first  the  former  course,  the  relation  of  each  part 
to  the  whole  will  be  touched  as  briefly  as  possible,  and  only  to 
make  each  part  as  intelligible  as  may  be. 

Locomotives  are  required  to  go  either  forward  or  backward  at 
will.  Hence  it  is  plain  that  if,  when  the  engine  is  at  rest,  the 
relative  position  of  the  slide  valve  T,T',T",  PI.  IV.,  Fig.  2,  and 
piston,  P,  is  such  that  steam  will  be  admitted  to  a  certain  side  of 
the  piston,  through  one  of  the  steam  passages,  and  will  make  the 


106  ELEMENTS   OF 

engine  go  one  way ;  then,  to  make  the  engine  go  the  other  war, 
the  valve  must  be  shifted  to  such  a  new  position  as  to  open  the 
opposite  steam  port  and  so  admit  steam  to  the  other  side  of  the 
piston,  instead. 

It  is  thus  also  plain,  without  tracing  here  all  parts  of  the  train 
of  pieces  from  the  driving  shaft  to  the  valve,  that  the  valve 
must  be  actuated,  in  the  two  cases,  either  by  two  different  posi- 
tions of  one  piece  made  to  take  hold  of  the  valve  spindle  or  its 
rocker-arm ;  or  else  by  two  different  suitably  disposed  pieces. 
In  the  latter  case,  which  is  the  one  employed  in  locomotive,  and 
many  other  engines,  these  pieces  may  be  either  separately  or 
simultaneously  acted  upon,  to  put  one  of  them  in  and  the  other 
out  of  gear  with  the  valve. 

In  Stephenson's  and  other  similar  link  motions  the  latter 
course  is  pursued.  The  two  Stephenson,  or  "  shifting "  links, 
one  on  each  side  of  the  engine,  are  raised  and  lowered  simul- 
taneously by  one  lever  in  the  engineer's  cab,  and  thus  the  valves 
are  actuated  so  as  to  produce  forward  or  backward  motion  at 
pleasure. 

The  link  and  its  attachments  are  thus  formed,  PI.  XVIL, 
Fig.  5.  LL  is  the  link,  which  is  an  open  or  slotted  curved 
bar.  The  link  is  embraced  by  a  saddle  block,  SS,  which  is 
sometimes  hung,  or,  as  in  the  figure,  bonie  up  by  the  supporting 
link  A.  In  either  case  the  link  A  is  attached  to  one  arm  of  a 
"  bell  crank,"  which  turns  on  a  fixed  shaft,  called  the  "  tumbling 
shaft "  (see  T,  PI.  IX.,  Fig.  3,  or  any  locomotive),  the  other  arm 
of  which  is  operated  on  from  the  "  foot-plate,"  where  the  driver 
stands,  to  raise  and  lower  the  link. 

F  is  the  link  block,  attached  to  the  lower  end  of  the  hanging 
rocker,  h,  Fig.  10,  by  the  pin  g,  and  on  which  the  link  freely 
slides  as  it  is  raised  or  lowered.  The  link  is  thus  rigidly  con- 
nected with  the  three  moving  points  P  and  Px,  the  eccentric 
rod  pins,  and  Q,  the  saddle  pin,  and  has  also  a  movable  connec- 
tion with  the  link  block  pin,  g,  whose  motion  depends  on  that  of 
the  link. 

Construction. — Leaving  further  details,  which  here  require 
too  much  to  be  imagined,  except  to  persons  already  familiar 
with  the  locomotive,  to  the  next  example,  and  mainly  until  valve 
motions  in  general  shall  be  described,  we  only  add  that  the- 
three  projections  in  Fig.  5  are  only  sketches  not  drawn  to  scale 
A  scale  of  from  one-third  to  one-sixth  would  be  appropriate. 


MACHINE   CONSTRUCTION   AND   DRAWING.  107 

C— SURFACE  COMMUNICATORS, 
a — Plane  Communicators. 

EXAMPLE  XXIX. 
A  Circular  Eccentric^  Strap,  and  Rod. 

Description. — A  circular  eccentric,  PL  XVIL,  Fig.  6,  gives 
rise  to  a  variable  rectilinear  motion. 

The  figure  shows  two  elevations  of  the  eccentric,  which  is 
made  in  two  pieces,  strongly  bolted  together,  at  bb,  on  one  side, 
through  the  projecting  halves  of  the  sleeve  IIHAF.  E — E  is  the 
eccentric,  bearing  the  rib  R—  R,  which  prevents  the  strap,  Fig. 

7,  from  slipping  off  laterally.     In  this  rib  is  the  oil  groove  g. 
Quite  small  eccentrics  are  solid  plates,  except  where  the  shaft 
to  which  they  are  fastened  goes  through  them.     This  one,  which 
belongs  to  a  locomotive,  is  open,  and  hence  stiffened  by  an  arm, 
a,  at  its  widest  opening.     In  putting  together  a  locomotive  valve 
motion,  the  eccentric  has  to  be  set,  as  will  be  more  fully  explained 
further  on,  so  as  to  give  the  desired  motion  to  the  slide  valve. 
This  is  done  partly  by  a  series  of  trials.     It  is  therefore  secured 
to  the  driving  shaft,  when   properly  adjusted,  by  set  screws 
through  the  holes  p  and  q. 

We  will  now  show  that  the  eccentric  is  a  substitute  for  a  short 
crank.  A  heavy  cranked  axle,  as  at  Fig.  9,  for  giving  a  very 
short  motion  as  a  valve  motion  =  2ac,  or  only  about  equal  to 
the  diameter  of  the  shaft  itself,  would  be  a  very  clumsy  and 
costly  device,  and  indeed  quite  impracticable  ;  first,  for  want  of 
room  if  the  axle  were  cranked  again  for  the  connecting  rod,  as 
in  engines  with  "  inside  connections ;  "  and  second,  because  the 
direction  of  the  valve  crank  arms  could  not  be  exactly  enough 
determined  in  advance. 

Now  let  O,  Fig.  6,  denote  the  centre  of  the  driving  shaft,  and 
centre  of  motion  of  the  eccentric ;  and  let  o  be  the  centre  of 
figure  of  the  eccentric.  Then  o  will  describe  a  circle  about  O, 
with  the  radius  Oo  /  and  any  fixed  point  on  the  eccentric  will 
describe  a  circle  about  O,  with  a  radius  equal  to  its  distance 
from  O.  Hence,  if  the  strap,  SS,  and  eccentric  rod,  a— a,  Fig. 

8,  were  rigidly  fastened  to  the  eccentric,  the  pin  a  would  describe 
a  circle  of  six  feet  radius,  more  or  less.     But  if,  as  is  done  in 
practice,  the  strap  is  secured  on  the  inner  circumference,  so  as 


108 

to  slide  freely  on  the  rib,  R,  of  the  eccentric,  then  the  pin  a  will 
be  actuated  back  and  forth  a  distance  equal  to  the  difference  of 
On  and  Om,  Fig.  6,  which,  since  the  eccentric  is  circular,  =  2O0. 
This  result  is  the  same  as  that  due  to  a  crank  of  the  length  Oo. 

An  eccentric  is  most  readily  conceived  of  as  essentially  a 
crank,  by  considering  it  simply  as  a  crank-pin  so  large  as  to  em- 
brace the  axle,  and  include  the  crank  arm  within  it.  The  eccen- 
tric strap  is  thus  seen  to  be  the  counterpart  of  the  strap  S,  Fig. 
1,  which  couples  the  stub-end  of  a  connecting  rod  to  a  common 
crank-pin. 

The  strap,  Fig.  7,  consists  of  two  irregular  semi-rings,  SRP  and 
SOK,  bolted  together  at  Ib.  To  the  upper  belongs  the  shoulder 
P  through  which  is  the  oil  passage  mn}  while  to  the  lower  seg- 
ment there  belongs  the  oil  well  O,  which  is  chambered  out  to 
f orm  a  reservoir  inside  ;  and  the  bearing,  K,  for  the  back  end, 
r,r,  of  the  eccentric  rod,  r— a.  From  the  two  measurements  of 
the  thickness,  an  edge  view  may  be  made  by  the  student. 

CO'  shows  a  portion  of  the  front  end  of  the  eccentric  rod 
where  it  takes  hold  of  the  link,  Fig.  5,  as  at  P  or  P'.  Here,  C 
is  a  plan  or  top  view,  and  C',  an  elevation  or  side  view. 

Construction. — After  the  full  description  just  given,  it  is 
enough  to  add  that  the  scale  may  range  from  one-half  to  oiie- 
eighth. 

Summing  up  now  the  valve  train  of  a  locomotive  in  a  skele- 
ton sketch,  we  have,  Fig.  36,  A,  the  driving  axle  ;  the  eccentrics 

s 


represented  by  their  centres  e  and  e' ',  and  crank  arms  eo  and 
e'o  /  the  eccentric  rods,  er  and  e'r  /  the  link,  L ;  link  block,  I  • 
fixed  rock  shaft,  R ;  hanging  and  standing  rockers,  RZ  and  Rs 
(IS) ;  valve  stem  or  spindle,  sv  ;  and  valve,  v,  on  its  seat  ff.  Ex. 
XLII.  Further  on  it  will  be  shown  how  to  lay  these  out  in  their 
proper  relative  positions  ;  though  the  student  can  exercise  him- 
self on  this,  with  measurements  from  practice,  and  with  certain 
fixed  data,  in  each  case,  learned  from  a  mechanic,  or  engine  driver. 


MACHINE   CONSTRUCTION   AND   DRAWING.  109 

EXAMPLE  XXX. 
A  Heart  Cam  or  Eccentric, 

Description. — This  cam  is  one  for  producing  a  uniform 
rectilinear  motion  from  a  like  rotat^y  one. 

The  distinction  between  a  cam  and  an  eccentric  is  perhaps 
not  very  closely  defined. 

It  may  be  said,  in  the  absence  of  fixed  usage,  that  a  cam 
wipes  or  pushes  againt  the  piece  which  it  acts  upon,  without 
being  actually  joined  to  it  by  a  material  connection.  Hence  it 
is  often  also  called  a  wiper.  An  eccentric,  on  the  contrary, 
may  take  hold  of  that  which  it  actuates. 

The  term  heart  eccentric,  above,  is  quite  indefinite,  since 
various  heart-shaped  curves  of  different  properties  may  be  de- 
vised. A  heart  eccentric  of  the  kind  here  required  will  be 
bounded,  on  its  acting  circumference,  by  parts  of  two  opposite 
spirals  of  Archimedes,  since  the  definition  of  that  curve  is, 
that  for  equal  angular  motions  of  its  generating  point,  the 
same  point  has  also  a  uniform  radial  motion. 

Construction. — Hence,  PL  XYIL,  Fig.  11,  let  it  be  required 
to  lift  and  let  fall  a  bar  vertically  through  a  space  of  9  inches, 
from  M  upwards.  Then  lay  off  from  M,  downwards,  the  least 
radius,  MO,  in  this  case  9  inches,  and  thence  the  greatest  ra- 
dius, OG,  which  must  be  9  inches  greater,  as  required,  or  18 
inches.  Divide  the  9  inches  from  G  upward  into  any  conve- 
nient number  of  equal  parts,  as  eight  (not  shown),  and  through 
the  points  draw  arcs  from  O  as  a  centre,  making  any  one  of  them 
a  complete  circle.  Divide  each  half  of  this  circle  into  eight 
equal  parts,  each  way  from  OG,  and  draw  radii  through  the 
points  of  division.  Then  M,  or  the  0  point  of  each  branch,  will 
be  the  intersection  of  the  innermost  or  0  circle,  with  OM,  the 
0  radius  ;  the  point  1  of  the  cam  will  be  the  intersection  of 
the  next,  or  circle  1,  with  the  next  radius,  0 1,  etc.,  on  each  side 
of  OG.  Through  the  points  thus  formed,  the  curve  can  be 
drawn  by  an  "  irregular  curve,"  or  by  circular  arcs,  if  desired, 
by  a  repeated  application  of  the  problem  "  to  draw  an  arc 
through  two  given  points,"  as  for  example  through  3  and  4,  and 
tangent  to  an  arc  through  the  points  0,  1,  and  1. 


110  ELEMENTS   OF 

Having  thus  found  the  outer  and  essential  curve  of  the  cam, 
the  parallel  inner  one  ACD  can  conveniently  be  drawn  tan- 
gent to  numerous  little  arcs  having  their  centres  in  M46G,  and 
a  common  radius  of  1  inch,  the  thickness  of  the  rim. 

The  construction  of  the  feathered  arms  is  obvious  enough  on 
inspection. 

The  vertical  section  through  MG  is  made  by  simply  project- 
ing over  from  the  curved  elevation,  and  laying  off  the  widths  of 
the  different  parts.  The  similar  letters  at  like  points  will  suffi- 
ciently explain  the  relations  of  the  two  figures. 

For  further  practice  let  the  student  make  a  horizontal  sec- 
tion through  O. 

b — Developable  Communicators. 

Gearing. 

81.  Before  entering  upon  the  construction  of  toothed  wheels, 
either  separately  or  as  acting  together,  a  few  preliminary  expla- 
nations of  the  principles  of  gearing  will  be  given,  which  may 
make  the  subject  more  intelligible,  yet  without  entering  into 
the  theory  of  the  subject  so  fully  as  would  be  done  in  a  work 
on  analytical  Cinematics. 

Gearing  is  the  term  commonly  applied  to  any  combination 
of  toothed  wheels ;  that  is,  wheels  fitted  with  teeth,  so  formed 
and  disposed  upon  their  circumferences  as  to  engage  each 
other  in  regular  order,  giving  a  desired  motion  to  the  wheels. 

82.  Gearing  may  be  classified :  first,  according  to  the  rela- 
tive positions  of  the  axes  of  the  wheels ;  second,  according  to 
the  disposition  of  the  teeth  relative  to  the  elements  of  the  con- 
vex surfaces  of  the  wheels. 

According  to  the  former  classification,  the  axes  may — 
I. — -Intersect  at  an  infinite  distance,  or  be  parallel. 
II. — Intersect  at  a  finite  distance,  or  simply  intersect. 
III. — Intersect  nowhere,  when  they  will  not  l>e  in  the  same 
plane. 

In  the  first  two  cases  the  axes  will  be  in  the  same  plane. 

83.  In  the  first  case,  the  wheels  mounted  on  the  parallel  axes, 
form  spur  gearing,  and  are  of  cylindrical  form,  PL  XX.,  Fig.  4. 

In  the  second  case,  the  wheels,  having  converging  axes,  are 
of  conical  form,  and  constitute  bevel  gearing,  PL  XX.,  Fig.  5. 


MACHINE   CONSTRUCTION    AND   DRAWING.  Ill 

In  the  third  case,  the  convex  surfaces  of  the  wheels  are 
frusta  of  hyperboloids  of  revolution  having  the  given  axes 
for  their  axes,  and  tangent  to  each  other  along  an  element ; 
that  is,  they  have  a  common  generatrix.  See  PI.  XX.,  Fig.  6, 
where  the  two  hyperboloids  represented  by  AB  and  CD  are 
tangent  along  the  common  element  mn. 

In  Fig.  4,  A  and  B  are  the  parallel  axes  of  two  thin  cylin- 
ders, in  contact  at  T,  and  from  which  the  finished  spur  wheels 
are  made. 

In  Fig.  5,  Y  is  the  common  vertex,  and  YT  the  common  gen- 
eratrix, or  element  of  contact,  of  two  tangent  cones,  YCT  and 
YDT,  whose  axes  are  YA  and  YB.  From  tangent  frusta,  as  TnC> 
and  T/iD,  of  these  cones,  a  pair  of  bevel  wheels  may  be  formed. 

In  Fig.  6,  AB  and  CD  represent  two  hyperboloids,  whose 
axes  are  AB  and  pq_,  and  whose  common  generatrix  and  ele- 
ment of  contact  is  mn.  Then  a  pair  of  thin  tangent  frusta,  as 
those  having  C  and  A  for  their  bases,  and  fitted  with  teeth  set 
in  the  direction  of  the  elements  of  the  respective  hyperboloids, 
will  act  together,  though  less  smoothly  than  in  the  two  preced- 
ing, cases,  since  the  tangents  niN  and  raK,  to  each,  at  their  point 
of  contact,  as  m,  will  not  coincide  ;  while  the  direction  of  the 
revolution  of  eacli  is  that  of  its  own  tangent. 

84.  By  the  second  classification  the  teeth  are  disposed  : — 

I. — In  the  direction  of  the  elements  of  the  surface  of  the 
wheel.  This  is  the  usual  case.  See  Pis.  XIX.,  XX.,  and  XXI. 

II. — Spirally,  as  in  PL  XXXI.,  Fig.  1,  2,  where  each  longitu- 
dinal edge  of  a  tooth  of  the  wheel  forms  part  of  a  very  long  helix, 
that  is,  a  helix  of  very  great  pitch. 

85.  Among  special  and  older  forms  of  gearing  are  the  lantern, 
Fig.  37,  where  pins,  generally  included  between  two  disks,  take 


the  place  of  teeth  of  the  usual  form.     These  may  be  seen  in 
common  brass  clocks.     Also  the  crown  wheel,  Fig.  38,  where 


112 


ELEMENTS    OF 


the  height  of  the  teeth  from  top  to  bottom,  instead  of  their 
length,  is  parallel  to  the  axis  of  the  wheel.  These  may  be  seen 
in  old  watches,  and  cider  mills. 

Small  toothed  wheels  engaged  with  much  larger  ones,  are  often 
called  pinions,  and  their  teeth  are  called  leaves.  In  small  work, 
especially,  the  axis  of  a  tooth  wheel  is  often  called  its  arbor. 

THEOREM  IX. 

The  number  of  revolutions  in  a  given  time,  and  the  angular 
velocities  of  toothed  wheels,  are  inversely  as  their  radii. 

Let  A  and  B,  Fig.  39,  be  two  cylinders  tangent  to  each  other, 
in  close  contact  along  the  element  whose  projection  is  C,  and 
mounted  on  the  shafts  also  indicated  by  A  and  B. 

So  long  as  there  is  only  a  rolling  motion,  without  slipping, 
between  their  circumferences,  both  of  their  convex  surfaces  will 
move  with 

Now  the  length  of  the 
circumference  varies  di- 
rectly as  the  radius.  If, 
then,  as  in  the  figure, 
BC=f  AC,  the  circumfer- 
ence of  wheel  B  will  be 
two- thirds  of  that  of  wheel 
A.  Therefore,  when  the 
two  wheels  are  made  to  re- 
volve, by  virtue  of  the  fric- 
tion between  them,  until  B 
has  made  one  entire  revo- 
lution, its  entire  convex 
surface  will  have  been  in 
contact  with  two-thirds  of 
the  circumference  of  A. 
That  is,  A  will  make  two- 
thirds  of  a  revolution,  for 
one  revolution  of  B  ;  that 
is,  the  number  of  revolu- 
tions of  each  wheel  is  in- 
Fia-  ®*'  versely  as  its  radius. 

Thus,  the  radius  of  A  being  f  of  that  of  B,  its  number  of 
revolutions  will  be  1  -f  =  f  as  many  as  those  of  B. 


MACHINE   CONSTRUCTION   AND   DRAWING.  113 

The  angular  space  swept  over  by  a  given  radius  of  each  wheel 
in  a  unit  of  time  measures  its  angular  velocity  /  and,  from  the 
explanation  just  made  about  the  comparative  revolutions  of  two 
wheels,  it  is  evident  that  their  angular  velocities  are  also  inversely 
as  their  radii. 

86.  It  is  quite  evident  that  but  little  power  could  be  trans- 
mitted from  A  to  B,  or  the  reverse.   In  other  words,  if  B  offered 
great  resistance  to  being  turned,  A  would  either  merely  slip 
upon  it  without  turning  it;  or,  if  the  two  wheels  were  very 
severely  pressed  together,  their  surfaces  of  contact  would  be 
speedily  ground  away. 

In  the  light  of  these  facts,  the  object  of  gearing  is  to  enable 
either  wheel  to  turn  the  other  against  a  great  resistance,  and  also  to 
preserve  the  same  relations  of  motion  that  have  just  been  stated. 

The  gearing  itself  consists  in  suitably-formed,  alternate  ribs 
and  grooves  on  the  surfaces  of  contact  of  the  two  cylinders,  so 
that  they  shall  not  merely  be  tangent  to  each  other,  but  shall 
take  hold  of  one  another.  Let  us  proceed  to  see  how  this  can 
be  done. 

87.  Since  cylinders  are  each  of  equal  cross-section  through- 
out, let  the  revolving  tangent  cylinders  be  represented  by  their 
circular  sections,  which  will  be  sufficient  for  all  purposes  of 
explanation.   Then,  with  A  as  a  centre,  Fig.  40,  which  is  double 
the  size  of  Fig.  39,  strike  two  circles,  AD  and  AE,  equidistant 
from  the  circle  AC,  within  and  without.     Do  the  like  with  B, 
as  a  centre  with  respect  to  the  circle  BC,  so  that  D  and  E  shall 
be  points  of  contact,  as  shown. 

Now  conceive  teeth  to  be  formed,  as  shown,  on  each  wheel, 
and  so  shaped  as  to  be  in  contact  at  C,  where  their  action  is 
most  effectual.  Also  let  them  be  so  shaped  as  to  begin  and  end 
their  contact,  as  at  n  and  o,  at  equal  distances  within  the  circles 
AC  and  BC.  Thus  the  average  distances  from  A  and  B,  of  all 
the  points  of  contact  of  the  teeth  which  are  in  contact  at  once, 
are  AC  and  BC.  Hence,  wheels  armed  with  such  teeth  will 
move  with  the  same  equal  velocity  at  C,  and  with  the  same 
relative  number  of  revolutions  as  did  the  original  tangent  cylin- 
ders, AC  and  BC. 

Again,  the  teeth  must  be  equal  in  width,  and  equally  dis- 
tributed on  the  two  wheels,  in  order  to  preserve  the  same  rela- 
tive velocity  between  the  two  wheels.  Hence  the  number  of 
8 


114  ELEMENTS   OF 

teeth,  on  each  wheel  will  be  directly  as  its  radius.  Thus,  if  BC 
=  |  of  AC,  and  if  the  wheel  A  has  24  teeth,  the  wheel  B  will 
have  16  teeth. 

88.  The  several  parts  of  the  teeth  and  their  governing  circles 
may  now  be  denned. 


The  circles  which  are  tangent  at  C,  and  which  represent  the 
original  cylinders  from  which  the  wheels  are  formed,  are  called 
pitch-circles. 

The  distance,  as  ab,  between  similar  points  of  two  successive 
teeth  is  the  pitch.  The  pitch  is  necessarily  the  same  on  any  two 
wheels  that  will  work  together. 

The  parts,  as  pp,  are  called  the  points  of  the  teeth ;  while  the 
lines,  as  at  R  and  R,  are  their  roots. 

The  circles  AF  and  BG  are  the  root-circles.  They  are  a  little 
within  the  circles  AD  and  BE,  so  that  the  points  of  the  teeth  of 


MACHINE    CONSTRUCTION   AND   DRAWING.  115 

one  wheel  shall  not  strike  the  rim  of  the  other  wheel  on  the 
spaces,  RT,  between  the  teeth. 

The  circles  AE  and  BD  are  the  point-circles. 

The  portions  of  the  sides  of  the  teeth,  as  at  pa,  are  the  faces  of 
the  teeth.  The  parts,  as  from  a  to  R,  are  \heflan7cs  of  the  teeth. 

The  spaces,  as  cb,  between  the  teeth,  are  a  little  greater  than 
the  widths,  as  ac,  of  the  teeth ;  both  distances  being  taken  on 
the  pitch-circle.  This  prevents  the  teeth  from  getting  wedged 
together. 

89.  It  is  now  necessary  to  describe  the  construction  and  some 
of  the  properties  of  a  class  of  curves,  which,  as  will  soon  be 
seen,  are  of  use  in  giving  the  true  forms  to  the  teeth  of  wheels. 

These  curves  are  the  cycloid,  epicycloid,  hypocycloid,  and 
involute. 

"When  any  curve,  A,  PL  XY1IL,  Fig.  1,  rolls  upon  any  other 
curve,  B,  any  point,  as  T,  of  the  rolling  curve  generates  or  de- 
scribes a  curve  of  the  class  called  Trochoids.  The  above- 
named  curves  are  merely  the  most  familiar  and  practically  use- 
ful trochoids.  In  their  formation,  either  the  rolling  or  the  fixed 
lines,  or  both,  are  circles.  Either  one,  but  not  both  at  once, 
may  be  a  straight  line. 

90.  The  common  cycloid,  or  simply  the  cycloid,  AK,  PL 
XVIII.,  Fig.  2,  is  the  curve  generated  by  any  point,  as  A,  of 
the  circumference  of  a  circle,  as  OA,  which  rolls  on  a  fixed 
straight  line,  AB.     If  the  rolling  curve  be  any  other  than  a 
circle,  the  curve  generated  will  still  be  a  cycloid,  but  the  above 
is  the  common  cycloid.    A  similar  remark  applies  to  each  of  the 
following  cases. 

91.  The  epicycloid,  AD,  PL  XVIII.,  Fig.  3,  is  generated  by 
a  point,  A,  of  a  circle,  AO,  which  rolls  upon  a  fixed  or  base 
circle,  AB.     The  two  circles  may  have  any  relative  size.     The 
epicycloid  has  two  varieties,  the   exterruil  epicycloid,  Fig.  3, 
where  the  centres,  Q  and  O,  of  the  given  circles  are  on  opposite 
sides  of  their  point  of  contact,  A ;  and  the  internal  epicycloid, 
Fig.  4,  where  those  centres  are  on  the  same  side  of  the  point  of 
contact.     In  the  latter  case,  the  rolling  circle  is  the  larger  one, 
and  its  concavity  rolls  upon  the  convexity  of  the  fixed  circle. 

92.  The  hypocycloid,  AK,  a7c,  AK',  PL  XVIII.,  Figs.  5, 
6,  is  the  curve  generated  by  a  point,  as  A,  or  a,  of  a  circle,  OA, 
which  rolls  on  the  interior  of  a  larger  fixed  circle,  AB. 

93.  The  involute,  AC,  PL  XVIII.,  Fig.  7,  is  the  curve  gen- 


116  ELEMENTS    OF 

erated  by  any  point,  A,  of  a  straight  line,  AD,  which  rolls  upon 
a  fixed  circle,  AB.  It  is  thus  the  curve  described  by  any  point 
of  a  thread  when  unwound  from  a  circular  plate.  This  is, 
strictly,  the  common  involute.  If  the  fixed  curve  be  any  other 
than  a  circle,  the  involute  would  be  an  involute  of  that  curve. 

The  construction  of  these  curves  by  points  will  now  be  ex- 
plained. 


PROBLEM  III. 
To  Construct  a  Cycloid. 

First  Construction.— Let  AB,  PI.  XVIIL,  Fig  2,  be  the  base 
line,  and  OA  the  rolling  circle.  By  the  definition  of  the  curve 
set  off  from  A,  on  the  circle,  spaces  0 — 1 ;  1 — 2,  etc.,  equal  to 
0 — 1 ;  1 — 2,  etc.,  on  AB.  When  the  corresponding  points,  as 
2,  2,  coincide  and  become  the  point  of  contact  of  the  circle  and 
base  line,  the  centre,  O,  will  be  at  the  point  2  on  the  line  CD, 
parallel  to  AB.  This  line  is  therefore  divided  in  the  same 
manner  as  AB.  Also  the  point  A  of  the  circle  will  then  have 
risen  to  the  same  height  above  AB  that  the  point  2d  now  has, 
and  hence  will  be  found  somewhere  on  the  line  cd,  through  2, 
and  parallel  to  AB.  The  like  is  true  for  other  points.  Hence 
take  the  successive  points  1,  2,  etc.,  on  OD  as  centres,  and  the 
constant  radius,  OA,  and  describe  arcs,  which  will  be  parts  of  the 
successive  positions  of  the  rolling  circle,  and  where  these  arcs 
intersect  the  horizontal  lines  1 — 1,  2 — 2,  etc.,  will  be  points  1, 
2,  3,  etc.,  of  the  cycloid. 

Second  Construction. — To  avoid  acute  and  indistinct  inter- 
sections, as  at  1  and  7  on  the  curve,  make  ab  =  cd,ef=  gh,  etc., 
to  find  the  points  of  the  curve,  instead  of  drawing  the  succes- 
sive positions  of  the  circle  OA. 

Fundamental  properties,  apparent  on  inspection.  First,  The 
distance  from  A  to  where  the  point  0  of  the  circle  again  coin- 
cides with  AB  is  evidently  equal  to  the  length  of  the  circum- 
ference of  the  rolling  circle.  Second,  The  extreme  distance, 
8 — 8,  of  the  curve  from  the  base  line  is  equal  to  the  diameter 
of  the  rolling  circle.  Third,  When  the  centre  O  moves  uni- 
formly on  OD,  the  generating  point,  0,  moves  most  rapidly,  both 
on  the  curve  and  in  the  direction  of  AB,  when  at  K,  as  is 
obvious  on  comparison  of  the  spaces  0 — 1 ;  1 — 2 


MACHINE   CONSTRUCTION   AND   DRAWING.  117 

7 — 8,  etc.,  on  the  curve,  which  correspond  to  the  equal  spaces 
0—1,  1—2,  etc.,  on  OD. 

PROBLEM  IY. 
To  Construct  an  Exterior  Epicycloid. 

Let  Q,P1.  XYIIL,  Fig.  3,  be  the  centre,  and  QA  the  radius  of 
the  base  circle,  and  let  OA  be  the  rolling  circle.  The  con- 
struction, as  may  now  be  seen  by  inspection,  is  so  exactly  analo- 
gous to  that  of  the  cycloid  that  detailed  description  is 
unnecessary.  0 — 1,  etc.,  on  the  circle  OA  =  0 — 1,  etc.,  on  AB. 
When  1,  2,  etc.,  on  AB  come  to  be  points  of  contact,  1,  2,  etc., 
on  OC  are  the  corresponding  positions  of  the  centre  of  the 
rolling  circle.  OC  is  drawn  with  QO  for  a  radius,  and  Q  1 — 1 ; 
Q2 — 2,  etc.,  are  its  successive  radii,  through  1,  2,  etc.,  on  AB, 
to  find  1,  2,  etc.,  on  OC.  Then,  as  in  the  cycloid,  the  point  2, 
for  example,  on  the  epicycloid  AD,  is  found  at  the  intersec- 
tion of  the  arc  2 — 2£  with  the  arc  having  the  centre  Q,  and 
radius  Qd  ;  or  by  making  ab  =  cd. 

The  fundamental  properties  are  the  same  as  those  mentioned 
in  the  last  problem. 

PROBLEM  Y. 
To  Construct  an  Interior  Epicycloid. 

Here,  again,  PI.  XYIIL,  Fig.  4,  the  construction  is  so  similar 
to  that  in  the  two  preceding  cases,  that  it  is  sufficient  to  point 
out  the  given  parts. 

The  circle  QB  is  the  fixed  base  circle.  The  circle  OA  is  the 
rolling  circle.  As  it  rolls,  its  centre  O  describes  the  circle  QO. 
The  points,  0, 1,  2,  etc.,  on  the  circle  QO,  are  the  successive 
positions  of  the  centre  O,  when  1,  2,  etc.,  on  the  circle  OA 
come  to  be  the  points  of  contact.  AD  is  the  epicycloid,  and, 
as  before,  when  2,  on  circle  OA  and  2  (w)  on  QA  unite  as  a 
point  of  contact,  A  will  have  removed  as  far  radially  from  the 
circle  QA,  as  2  on  OA  now  is  from  the  circle  QA.  Hence  A 
will  be  found  on  the  arc  2 — 2,  having  Q  for  its  centre,  and  at 
its  intersection  with  2 — 2  having  (&)  2,-  on  circle  QO  for  its 
centre.  Or,  as  before,  make  ab  =  cd  and  ef=gh,  to  find  the 
points  3  and  4,  for  example,  of  the  epicycloid. 


118  ELEMENTS    OF 

The  secoiid  property  in  Prob.  IY.  must  here  be  modified  to 
read,  that  the  extreme  distance  of  this  epicycloid  from  the  base 
circle  will  be  equal  to  the  difference,  BK,  of  the  diameters  of 
the  rolling  and  base  circles. 

PROBLEM  VI. 
To  Construct  any  Hypocycloid. 

The  construction,  PI.  XVIIL,  Figs.  5,  6,  is  again  so  closely 
analogous  to  the  preceding  cases,  that  it  only  seems  necessary 
to  point  out  the  different  cases.  AK,  Fig.  5,  is  the  hypocycloid 
generated  by  the  point  A  of  the  circle  OA  rolling  from  A 
towards  B  on  the  inner  side  of  the  circumference  QA.  The 
circle  OD  is  the  path  of  the  centre,  O,  of  the  rolling  circle. 
Equal  distances,  0 — 1 ,  etc.,  =  0 — 1,  etc.,  are  laid  off  from  A  on 
both  circles,  and  any  point,  as  4,  of  AK,  can  be  found  at  the  in- 
tersection of  the  arc  as  4 — 4,  with  centre  Q,  and  the  arc,  as 
4 — 4j  with  centre  4  on  OD ;  or  by  making  ab=cd.  Observe 
that  when,  as  in  this  case,  the  radius,  OA,  of  the  rolling  circle, 
is  more  than  half  of  QA,  that  of  the  base  circle,  the  hypocy- 
cloid, AK.  and  the  motion  of  the  circle  OA,  are  on  opposite  sides 
of  the  initial  ra'dius  OA. 

In  the  same  figure,  ok  is  the  hypocycloid,  constructed  just  as 
before,  generated  by  the  point  a,  of  the  circle  oa,  which  rolls 
towards  J,  on  the  inner  side  of  the  circumference  Qa.  Here,  where 
the  radius  of  oa  is  less  than  half  of  Q#,  the  motion  of  the  circle 
Oa,  and  the  hypocycloid,  ak,  are  both  on  the  same  side  of  the 
initial  radius  oa.  This  result  prepares  the  mind  to  apprehend 
the  intermediate  case,  shown  in  Fig.  6,  where  the  radius,  OA, 
of  the  rolling  circle  is  just  half  of  QA,  that  of  the  base  circle, 
and  the  hypocycloid  becomes  a  diameter  AK. 

The  fundamental  properties  mentioned  in  Prob.  III.  hold 
good  for  the  hypocycloids. 

PROBLEM  VII. 
To  Construct  the  Involute  of  a  Circle. 

Let  the  circle  OA,  PL  XVIIL,  Fig.  7,  be  the  fixed  circle, 
and  AD  the  straight  line  which  rolls  upon  it.  As  in  the  pre- 


MACHINE   CONSTRUCTION  AND   DRAWING.  119 

ceding  problems,  the  rolling  spaces  of  AD,  and  the  correspond- 
ing circular  arcs  rolled  upon,  are  necessarily  equal.  Hence  set 
off  equal  distances,  from  A  on  AB  ;  draw  a  tangent  to  the 
circle,  at  each  of  these  points ;  and  then,  with  1  on  AB  as  a 
centre,  and  1 A  as  a  radius,  describe  the  arc  A#  to  intersect  the 
tangent  1 — 1  at  a.  With  2,  on  AB,  as  a  centre,  and  2 — a, 
as  a  radius,  describe  the  arc  ab,  giving  5  on  the  tangent  2 — 2. 
In  like  manner  any  number  of  points  on  the  involute  AC  may 
be  found.  AC,  as  thus  found,  is,  of  course,  not  a  perfectly  true 
involute,  since  the  radius  of  the  latter  should  change  at  each 
instant;  but  neglecting  the  slight  error  of  taking  the  chords 
1 — A;  2 — 1,  etc.,  on  AB  as  equal  to  their  arcs,  the  points 
a,  h,  3,  etc.,  of  the  involute  are  exact. 


THEOREM  X. 

In  all  the  curves  just  described,  the  tangent,  at  any  point,  is 
perpendicular  to  the  line  from  that  point  to  the  corresponding 
point  of  contact  of  the  rolling  and  fixed  lines. 

This  theorem  becomes  evident  by  simply  considering  that 
the  rolling  circles  are  of  an  invariable  form  and  size,  and 
hence,  as  in  PI.  XVIII.,  Fig.  2,  afford  a  geometrically  inflexible 
connection  between  any  point,  as  4,  of  the  cycloid,  etc.,  and 
the  corresponding  point  of  contact,  4,  on  AB.  That  is,  the 
chord  mt  (ft,  Fig.  3)  is  a  fixed  line  for  the  instant  that  t  is  the 
point  of  contact  of  the  rolling  circle  and  base  line.  In 
other  words,  m  (/")  is  at  the  same  instant  about  to  describe  a 
circular  arc  about  t  as  a  centre.  Hence  a  perpendicular  to  mt, 
at  m,  will  express  the  direction  of  this  instantaneous  circular 
effort,  and  will,  therefore,  be  the  tangent  at  m. 

Like  reasoning  applies  to  Figs.  3,  4,  and  5.  In  the  case  of  the 
involute,  the  point  J,  for  example,  evidently  tends  for  the  in- 
stant to  describe  a  circular  arc  about  2,  on  AB,  as  a  centre. 
That  is,  the  tangent  to  the  involute  at  &  is  perpendicular  to  the 
line  lc. 

THEOREM  XI. 

The  relative  position  of  two  circles  is  the  same,  whether  one 
rolls  over  a  certain  arc  of  the  other,  which  is  fixed,  or  both  re- 


120  ELEMENTS   OF 

volve  on  fixed  centres  till  they  have  had  the  same  amount  of 
contact  as  before. 

Let  the  circle  A,  PI.  XYIIL,  Fig.  8,  roll  over  the  arc  G'C', 
on  the  circle  B,  which  shall  be  fixed.  C'D',  etc.,  =  c'd',  etc. ; 
C'G'  =  c'g',  and  the  radius  AG'  will  be  found  at  Ay.  Now 
turn  the  entire  system  about  B  as  a  centre  till  the  line  of 
centres  BA'  has  returned  to  its  original  position,  BA.  The 
point  g'  will  then  appear  at  g  ;  A!  at  A ;  c'g'  at  Cjjf  /  C'G'  at 
CG ;  ^AB  will  be  equal  to  /A'B,  and  G'g  =  CG.  But  the 
latter  result  is  just  that  which  follows  from  the  revolution  of  A 
and  B  on  their  centres,  while  in  contact,  without  slipping,  at  C. 

Thus  the  relative  position  of  the  two  circles  in  the  two  cases 
is  the  same,  as  stated  in  the  theorem. 


THEOREM  XII. 

The  relative  position  of  three  circles,  which  maintain  a  com- 
mon point  of  contact,  is  the  same,  whether  one  of  them  is  fixed, 
or  all  revolve  on  their  centres. 

Let  B,  0,  and  A,  PI.  XYIIL,  Fig.  9,  be  the  centres  of  the 
three  circles.  If  A  roll  on  B,  from  D  to  D',  we  shall  have 
d"d'  =  DD',  and  every  point  of  d"d'  will  have  been  in  contact 
with  DD'.  If  the  circles  C  and  A  maintain  the  same  point  of 
contact,  d,  that  point  will  be  found  at  d',  and  0  at  C'.  If,  then, 
the  circle  C  roll  from  its  position  C'd'  to  C"d",  we  shall  have 
d"d""  =  d"d'  =  D'D.  Hence,  if  circle  C  roll  on  B  from  D 
to  D',  we  shall  have  d"d""  =  D'D  =d"d'.  Thus,  when  the 
centres  B,  C,  and  A  have  in  this  manner  reached  B,  C",  and  A', 
the  circle  C  has  virtually  rolled  on  the  exterior  of  B,  and  the 
interior  of  A,  and  over  an  equal  length  of  arc  on  each. 

Now  revolve  the  entire  system  about  B  as  a  centre,  from  the 
position  BC"A'  to  BOA,  and  D'D  will  appear  at  DD"  ;  d"d' 
at  dd'",  and  d"d""  at  ddv,  and  we  shall  have  DD"  =  dd'"  = 
dd'.  But  the  result  DD"  =  ddv  is  just  what  follows  from  the 
revolution  of  B  and  C  on  their  centres  with  purely  rolling  con- 
tact at  d.  Also  DD"  =  dd'"  expresses  a  like  motion  of  B  and 
A,  and  ddv  =  dd'"  a  like  motion  of  C  on  the  interior  of  the 
circumference  of  A ;  which  satisfies  the  enunciation. 


MACHINE   CONSTRUCTION   AND   DRAWING.  121 


THEOREM   XIII. 

In  the  rolling  of  three  circles,  with  a  common  point  of  con- 
tact, any  point  of  the  inner  circle  will  describe  an  epicycloid 
upon  the  circle  on  which  it  rolls,  and  a  hypocycloid  within  the 
remaining  circle.  These  curves  will  be  the  proper  curves  for 
teeth,  acting  tangent  to  each  other,  to  give  a  rolling  motion  to 
the  circles  to  which  they  belong. 

The  separate  motions  of  the  pairs  of  circles,  B  and  A,  PL 
XYIIL,  Fig.  10,  being  seen,  when  analyzed,  to  be  as  explained 
as  in  the  last  theorem,  it  is  clear  that  the  point  of  contact,  m  (d, 
Fig.  9),  of  the  inner  circle,  A,  will  describe  an  epicycloid,  as 
Q'A'  on  the  circle  B,  which,  after  revolution  of  the  system  from 
BE'  to  BE  (BA'  to  BA,  Fig.  9),  will  appear  at  Qh.  Also  that 
the  same  point  of  contact,  m,  when  circle  A  rolls  from  A"  to  A' 
(circle  C,  Fig.  9,  from  C'  to  C",  or,  what  is  the  same,  from  C'"  to 
C),  will  describe  the  hypocycloid  d'h ',  which  appears  at  dh. 
But  note  that  for  the  three  circles  to  have  constantly  a  common 
point  of  contact,  is  for  A  to  roll  simultaneously  upon  B,  and 
within  E.  Hence  the  point  m  of  the  circle  A  simultaneously 
generates  the  epicycloid  Q'A'  (QA)  and  the  hypocycloid  d'h' 
(dh).  These  curves,  thus  having  at  each  instant  one  common 
point,  will  therefore  be  constantly  tangent  to  each  other  at  the 
position  for  the  moment  of  that  point.  And  as  their  common 
normal  constantly  passes  through  the  common  point  of  contact 
of  the  three  circles  by  Theorem  X.,  as  mh  passes  through  m,  it 
follows  that  the  constant  contact  of  QA  with  dh  will  maintain  a 
constant  contact  of  the  circles  B  and  A.  For  h  and  q  are 
always  at  the  same  distance  from  m,  on  the  same  line  m  (gh). 

We  have  now  the  following  fundamental  theorem  of  gearing. 


THEOREM  XIV. 

When  any  circle,  less  than  either  of  two  given  pitch-circles, 
rolls  on  the  exterior  of  loth,  and  on  the  interior  of  loth,  it  will, 
in  the  former  case,  generate  the  faces  of  the  teeth  of  loth  wheels, 
and  in  the  latter  their  flanks. 

This  theorem  is  little  more  than  a  slight  expansion  of  the 
preceding,  expressed  in  technical  terms.  The  epicycloid  QA. 


122  ELEMENTS    OF 

PI.  XYIIL,  Fig.  10,  being  external  to  the  pitch-circle,  B,  any 
small  portion  of  it,  limited  by  a  point-circle,  concentric  with  B, 
and  a  little  larger  than  it,  would  be  a  face  of  a  tooth  of  B. 
Likewise  the  hypocycloid,  dh,  being  internal  to  the  pitch-circle 
R,  a  small  portion  of  it  between  that,  circle  and  a  concentric 
root-circle  (88)  within  it  would  be  the  jfftm&  of  a  tooth  of  R. 

Now  it  is  obvious  that,  if  the  same  circle  A  were  to  roll  upon 
R  and  within  B,  similar  results  to  the  foregoing  would  follow ; 
which  proves  the  theorem ;  since,  by  the  last  theorem,  these 
curves  would  always  have  a  point  of  contact. 

The  circle,  as  A,  Fig.  10,  which  thus  carries  the  generating 
point  of  the  tooth-curves,  is  called  the  describing  circle. 


THEOKEM  XV. 

Involutes  are  proper  curves  for  the  teeth  of  wheels. 

A  general  proof  of  this  would  be  that  the  rolling  straight 
line  EN,  PI.  XVIIL,  Fig.  11,  any  point  of  which  generates  an 
involute,  is  but  the  extreme  case  of  the  rolling  circle,  viz.,  that 
in  which  the  radius  is  infinite.  But  the  generating  line  does 
not  roll  directly  upm  the  pitch-circles,  since  the  teeth  would 
then  be  wholly  exterior  to  the  pitch-circles.  Hence  the  gen- 
erating line  is  taken,  as  at  EN,  tangent  to  base-circles  within 
the  pitch  circles  of  the  wheels,  and  containing  the  point  of  con- 
tact. Any  point,  as  d,  on  the  line  EX,  will  then  generate  the 
involute,  de,  of  the  base-circle,  BN,  of  the  wheel  B ;  and  the 
involute  dfo£  the  base-circle,  AE,  of  the  wheel  A. 

Any  other  point,  as  n,  will  generate  the  involutes  F  and  G. 
Now,  as  all  involutes  of  the  same  circle  are  equal  curves,  and  as 
the  common  generatrix  of  both  involutes,  whether  d  or  n,  is  on 
the  line  EN,  the  point  of  contact  of  any  given  pair  of  involutes 
will  be  on  EN,  and  thus  F  and  G  may  simply  be  regarded  as 
new  positions  of  the  involutes  f  and  e,  caused  by  a  rotation  of 
the  circles  having  A  and  B  for  their  centres. 

Now  this  result  secures  a  rolling  contact,  or  an  equal  velocity 
of  circumference,  at  C,  and  hence  an  angular  velocity  of  each 
wheel  inversely  as  its  radius,  for  we  have  by  the  definition  of 
the  involute 

e&  =  eS  —  M  =  dN  —  nN  =  En  —  Ed=E'F  —  Er  =  rF', 
or,  ek  =  rF ;  that  is,  the  circumference  velocities  of  E  and  N 


MACHINE   CONSTRUCTION   AND    DRAWING.  123 

are  equal.  But,  by  the  similar  triangles,  AEG  and  BNC,  the 
radii  of  the  pitch-circles  are  to  each  other  as  the  radii  of  the 
base-circles.  Hence  the  circumference  velocities  of  the  pitch- 
circles  also  are  equal,  which  secures  their  rolling  contact  at  C, 
as  stated  and  required. 


THEOREM  XYI. 

The  teeth  act  by  sliding  contact,  and  their  point  of  contact 
is  on  the  generating  line. 

First,  That  the  teeth  of  wheels  act  by  sliding  contact 
is  evident  from  PL  XYIIL,  Fig.  10,  where,  when  the  wheels 
A  and  B  revolve  through  the  arc  MQ=m<#,  the  portion,  Q^,  of 
the  face  curve  of  the  teeth  of  B  has  been  in  contact  with  every 
point  of  dh,  since  both  are,  as  before  shown,  generated  simul- 
taneously by  the  same  point  m.  But  Q^  being  obviously 
much  longer  than  dh,  there  must  have  been  a  sliding  contact 
between  them,  equal  to  the  difference  of  their  lengths.  The 
same  property  is  evident  in  the  action  of  involute  teeth,  PL 
XVIIL,  Fig.  11,  since,  for  the  instant  in  which  all  parts  have 
the  position  there  shown,  the  velocities  of  d  as  a  point  of  dN, 
generating  de,  and  as  a  point  of  dE,  generating  fr,  are  as  the 
momentary  radii  dN  and  dE. 

/Second,  The  point  of  contact  of  the  tooth  curves  is  always 
on  the  generating  circle,  simply  because  one  and  the  same  point 
of  that  circle  is  the  common  generatrix  of  both. 


THEOREM  XVII. 

Teeth,  formed  by  either  of  the  preceding  methods,  give  a  con- 
stant angular  velocity  ratio  to  the  wheels  which  carry  them. 

This  has,  in  effect,  been  already  shown  for  wheels  with  in- 
volute teeth,  PL  XVIII.,  Fig.  11,  by  means  of  the  similar  tri- 
angles AEG  and  BNC,  in  which  EN  constantly  passes  through 
C,  and  therefore  BC  and  AC,  the  radii  of  the  pitch-circles,  are 
constant  segments  of  the  line  of  centres,  and  always  propor- 
tional to  BN  and  AE,  which  are  constant. 

For  the  case  of  epicycloidal  teeth,  see  PL  XVIII.,  Fig.  10. 


124  ELEMENTS   OF 

Now,  first,  by  Theor.  X.,  and  since  the  tooth  curves  are  in  con- 
tact at  the  position,  for  the  moment,  of  the  common  generatrix 
h,  of  dh,  and  q  of  Q^,  their  common  normal  constantly  passes 
through  M,  the  point  of  contact  of  the  pitch  circles. 

Second,  to  maintain  contact  as  at  qh,  all  points  of  the  indefi- 
nite common  normal,  he,  must  at  each  instant  be  moving  with 
the  same  velocity  in  the  direction  of  that  line.  Hence  the  an- 
gular velocities  of  r  and  e  are  as  the  radii,  Kr  and  l$e,  drawn 
perpendicular  to  that  line.  But  the  ratio  B<?  :  Jlr  is  constant, 
since  those  lines  are  proportional  to  BM  and  KM,  which  are 
constant.  That  is,  the  ratio  of  the  angular  velocities  of  points 
r  and  e,  whose  velocities  are  determined  by  the  action  of  the 
teeth,  is  constant ;  and  therefore  that  of  the  pitch  circles  is  so 
also,  because  the  common  normal  divides  the  line  of  centres  into 
constant  segments,  by  passing  always  through  the  point  of 
contact  of  the  pitch  circles. 

94.  The  wheel  which  actuates  the  other  is  called  the  driver. 
The  other  is  called  the  follower. 

When  the  wheels  revolve  so  that  B,  PI.  XVIII.,  Fig.  10, 
turns  to  the  right,  the  pitch  circle  arc,  as  QM,  through  which 
action  takes  place  between  the  tooth  curves,  beginning  at  q,  is 
called  the  are  of  approach.  If  the  wheels  should  revolve  so 
that  B  should  turn  to  the  left,  the  same  arc  would  be  termed 
the  arc  of  recession,  since  it  is  the  arc  through  which  action  takes 
platfe  while  the  points  M  and  m  are  receding  from  the  line  of 
centres  to  the  positions  of  Q  and  d.  The  sum  of  the  two  is  the 
arc  of  action. 


THEOREM  XVIII. 

Within  certain  limits,  the  face  of  a  driver  acts  best  upon  the 
flank  of  a  follower,  and  during  the  arc  of  recession  •  but  for 
either  of  a  pair  of  wheels  to  be  a  driver,  the  teeth  of  each 
must  have  both  faces  and  flanks. 

Since  the  face  of  the  driver  acts  upon  thejfa^l'  of  thefol- 
lower,  during  the  arc  of  recession,  it  follows  that,  if  the  motion 
be  reversed,  so  that  in  PL  XVIII.,  Fig.  10,  for  example,  the 
circumferences  of  the  pitch  circles,  E  and  B,  shall  roll  to  the 
right,  through  M,  the  former  arc  of  recession,  when  motion 


MACHINE   CONSTRUCTION   AND   DRAWING.  125 

was  to  the  left  through  M,  will  become  the  arc  of  approach,, 
and  the  flank,  dh,  of  the  wheel,  H,  will  push  the  face,  Q^,  of 
the  wheel  B. 

Now:  First.  It  is  found  experimentally  that  the  friction 
between  the  teeth  is,  at  least  within  certain  limits,  more  abrasive 
and  vibratory  during  the  arc  of  approach  than  during  the  arc 
of  recession.  Hence,  if  one  of  a  pair  of  wheels  were  to  be 
only  and  always  a  driver,  it  would  be  desirable  that  its  teeth 
should  only  have  faces,  and  the  other  wheel's  teeth  only 
flanks.  But  it  is  also  important  that  any  one  pair  of  teeth 
should  not  quit  contact  with  each  other  before  another  pair 
should  come  into  contact.  Indeed,  to  distribute  the  pressure 
better,  two  or  more  pairs  of  teeth  should  be  in  contact  at  once. 
Now,  if  this  last  condition  be  fulfilled  in  the  arc  of  recession 
alone,  it  might  require  teeth  so  long  as  to  make  the  friction  be- 
tween them  as  severe  as  during  the  arc  of  approach.  This  is 
evident  by  comparing  the  spaces  5 — 6,  on  the  curves,  in  PL 
XVIII.,  Figs.  3  and  5,  with  the  point  #,  Fig.  10.  For  the  gen- 
eratrix of  the  epicycloid,  Fig.  3,  moves  as  there  seen  with  rapid- 
ity, but  that  of  the  hypocycloid,  Fig.  5,  with  slowly  increasing 
velocity.  Hence,  Fig.  10,  there  is  more  sliding  contact  between 
h  and  q,  than  when  Q  and  d  are  in  contact. 

Hence,  as  a  balancing  of  advantages  of  action,  as  well  as  to 
allow  either  wheel  to  drive,  both  wheels  have  teeth  having  both 
faces  and  flanks. 

Second.  That  the  action  of  a  face  of  the  driver's  tooth  upon 
the  fomk  of  a  follower's  tooth  takes  place  in  the  arc  of  recession, 
is  evident  from  Fig.  10.  Let  the  wheels,  R  and  B,  revolve,  so 
that  their  circumferences  shall  move  to  the  right  through  Q', 
until  the  initial  points,  Q  and  d,  of  the  indefinite  tooth  curves 
shall  have  passed  beyond  Q'.  Their  curves  will  then  no  longer 
be  in  contact,  but  let  the  wheels  revolve  to  the  left,  and  these 
curves  will  begin  contact  at  ra  /  Q'^'  acting  against  dh,  then  at 
mk,  since  m  is  the  initial  position  of  their  common  generatrix, 
and  will  continue  in  contact  in  departing  from  the  line  of  cen- 
tres AB,  to  the  left,  till  one  or  the  other  curve  is  limited. 

95.  The  proportions  practically  adopted  by  millwrights  are 
grounded,  whether  intentionally  or  not,  on  a  proper  balancing 
of  the  foregoing  principles. 

As  differently  given,  these  proportions  are  as  follows : — 


126  ELEMENTS   OF 

Pitch  =  1. 

5         7 

Width  of  tooth  on  pitch  circle  =  —  or  — 

11         15 

60 
o 

space     '  —        or  — 

11         15 

3          5i!r 
Radial  length  of  tooth  face  =  —  or  ~ 


96.  For  wheels  of  very  few  teeth,  the  teeth  should  be  longer 
than  these  proportions  give,  in  order  to  afford  a  sufficient  arc  of 
action.     The  common  generatrix  of  the  tooth  curves  being  on 
the  describing  circle  as  A,  PI.  XVIIL,  Fig.  10,  or  straight  line, 
as  E2T,  Fig.  11,  the  teeth  may  be  limited  by  simply  assuming 
any  point,  as  n,  Fig.  10,  or  d,  Fig.  11,  according  to  the  direction 
of  rotation  considered,  where  contact  shall  begin  or  end,  and 
drawing  the  point  circle  of  the  wheel,  as  B,  through  that  point. 

97.  When  the  describing  circle  of  the  teeth  is  equal  to  either 
given  pitch  circle,  the  hypocycloid  generated  by  a  given  point 
of  it  reduces  to  that  point  itself,  since  evidently  no  rolling  mo- 
tion of  the  describing  circle  can,  in  that  case,  take  place  within 
the  equal  pitch  circle. 

98.  We  have  now  all  the  data  necessary  for  determining  the 
forms  of  the  teeth  of  wheels,  on  any  given  pitch  circles,  or  lines, 
as  in  the  case  of  a  rack.    Moreover,  if  we  consider  a  bevel  wheel 
as  composed  of  indefinitely  thin  laminse,  of  decreasing  size,  and 
perpendicular  to  the  axes  of  the  wheels,  any  two  corresponding 
laminae  may  be  regarded  as  a  pair  of  spur-wheels,  whose  teeth, 
at  the  principal  point  of  contact,  i.e.,  on  the  element  of  contact 
of  the  pitch  cones,  will  be  in  the  same  plane.     And  if  we  fur- 
ther regard  a  spiral  gear  (84)  as  composed  of  such  laminae,  each 
set  an  indefinitely  small  distance,  angularly,  in  advance  of  the 
preceding  one,  these  laminae,  also,  will   be  merely  thin   spur 
wheels.     And,  finally,  plane  sections  of   hyperboloidal  wheels, 
perpendicular  to  their  axes,  and  through  a  common  point  on  the 
element  of   contact  of  the  pitch  hyperboloids,  will  be  simply 
spur  wheels,  only  not  lying  in  the  same  plane. 

Hence  the  foregoing  principles  are  sufficient  for  every  case 
with  which  we  have  to  do. 

99.  These  cases  are  as  follows,  for  all  forms  of  spur  gearing; 


MACHINE   CONSTRUCTION   AND   DRAWING.  127 

and  the  solution  in  each  case  follows  directly  from  Theorems 
XIY.  and  XY.,  or  from  the  simple  modifications  which  result 
from  making  the  describing  circle  equal  to  half  of  a  pitch 
circle,  or  equal  to  a  pitch  circle,  or  infinite,  i.e.,  a  straight  line, 
as  in  involute  teeth. 

I. — General  Solution. 

1.  Common  Spur-wheels — PI.  XXI.,  Fig.  4. — In  the  general 
case,  use  the  same  describing  circle,  D,  for  both  wheels,  making 
its  diameter  less  than  the  radius,  BT,  of  the  least  pitch  circle, 
Theor.  XIV.,  in  order  that  convex  faces  may  act  against  concave 
flanks.      Then   the  faces  of  their  teeth   will   be    the   epicy- 
cloids generated  by  a  point,  as  T,  of  D,  when  rolling  on  the 
exterior  of  each  pitch  circle ;  and  their  flanks  will  be  the  hypo- 
cycloids  generated  by  a  point,  as  T,  of  the  same  circle,  when 
rolling  on  the  interior  of  the  pitch  circles. 

2.  A  Spur-wheel  with  an  Annular  Wheel. — The  teeth  of  the 
spur-wheel  would  l)e  formed  as  in  the  preceding  case.     The 
pitch  and  point  circles  of  the  annular  wheel,  PI.  XXI.,  Fig.  7, 

.  would  be  within  its  root  circle,  and  the  faces  of  its  teeth  will 
be  hypocycloids,  and  their  flanks,  epicycloids. 

Thus,  the  face,  Te,  of  the  spur-wheel  is  generated  by  the 
point  T  of  the  circle  D,  rolling  on  the  exterior  of  the  pitch 
circle  Tp''  The  flank,  Tc,  of  B,  is  generated  by  T  as  D  rolls 
within  Tp'.  The  face,  T£,  of  A,  is  a  hypocycloid  generated  by 
T  as  D  rolls  within  Tp,  the  pitch  circle  of  A ;  and,  finally,  the 
flank,  T#,  is  generated  by  T  as  D  rolls  on  the  convex  side  of  Tp. 

3.  Spur-wheel  and  Rack. — The  spur-wheel   teeth   being  as 
before,  both  faces  and  flanks  of  the  rack  teeth  will  be  cycloids, 
generated  by  the  rolling  of  the  same  describing  circle  on  both 
sides  of  its  pitch  line.     The  student  can,  therefore,  readily  con- 
struct a  diagram  of  this  case,  which  should  be  made  to  scale 
from  assumed  measurements.     This  can  be  done  after  reading 
the  example  of  the  spur-wheel. 

II. — The  Describing  Circle  equal  to  half  the  Pitch  Circle. 
1.  Spur-wheels. — In  this  case,  the  flanks  of  the  teeth  of  both 


128  ELEMENTS    OF 

wheels  will  be  radial  and  straight,  as  in  PI.  XIX.  The  faces 
will  be  epicycloids,  and,  by  Theor.  XIV.,  the  faces  of  either 
wheel,  and  the  flanks  of  the  other,  will  have  the  same  describing 
circle. 

Such  wheels  may  be  more  easily  made,  but  they  have  the  dis- 
advantage over  those  formed  by  the  general  solution,  which  is 
shown  in  the  following — 


THEOREM  XIX. 

Any  two  wheels  of  the  same  pitch,  formed  by  the  general 
solution,  with  a  constant  describing  circle,  will  work  together  / 
but  one  made  by  the  second  solution  will  work  perfectly  only 
with  those  of  one  other  number  of  teeth,  and  the  same  pitch. 

To  prove  this,  suppose  a  wheel,  A,  of  40  teeth,  to  be  adapted 
to  work  with  one,  B,  of  50  teeth.  The  describing  circle,  a,  for 
the  faces  of  B  to  act  upon  the  flanks  of  A,  Theor.  XIV.,  will 
have  for  its  diameter  the  radius  of  A.  'Now  let  C  be  a  wheel  of 
70  teeth,  and  of  the  same  pitch  as  A  and  B  have. 

Then  the  faces  of  B,  to  act  upon  the  radial  flanks  of  C,  should 
be  epicycloids  generated  by  a  point  of  a  different  describing 
circle,  c,  whose  diameter  will  be  equal  to  the  radius  of  C.  Thus 
the  faces  of  B  will  be  different,  according  as  it  is  to  drive  A  or 
C.  But  by  the  general  solution  both  faces  and  flanks  of  all  the 
wheels  are  formed  by  a  point  of  the  same  describing  circle,  hence 
any  two  of  them,  of  the  same  pitch,  will  work  together. 


2.  Spur-wheel  and  Rack. — Let  A  be  the  pitch  line  of  the  wheel, 
and  B  that  of  the  rack.     Let  CT  be  the  describing  circle  for 


MACHINE   CONSTRUCTION   AND   DRAWING.  129 

the  faces  of  the  rack  gndj£0tt£0  of  the  wheel.  Then  the  former, 
ab,  will  be  cycloids,  and  the  latter,  radii  of  the  circle  OA. 

Now,  under  the  same  solution,  the  radius  of  the  rack  pitch 
line  being  infinite,  the  radius  of  its  describing  circle  will  be 
infinite  also,  and  this  circle  will  coincide  with  BT.  Hence  the 
radial  flanks,  ac,  of  the  rack  will  become  perpendicular  to  BT, 
and  the  faces  of  the  wheel,  being  generated  by  a  point  of  BT, 
will  be  involutes  of  the  pitch  circle  OA.  By  Theor.  XYI.  the 
contact  of  the  teeth  will  be  in  the  line  BT,  during  the  arc  of 
approach,  when  the  rack  drives  ;  and  during  the  arc  of  reces- 
sion when  the  wheel  drives.  Thus,  during  a  part  of  the  action, 
the  teeth  come  in  contact  only  at  a  single  point  of  each,  which 
is  disadvantageous,  by  occasioning  unequal  wear. 

The  application  to  annular  wheels  is  too  obvious  to  need  de- 
tailed rehearsal.  The  student  can  construct  the  case. 


III. — The  Describing  Circle,  equal  to  one  of  the  Pitch  Circles. 

1.  Pin-wheel  and  Spur-wheel. — Let  A  and  B  be  the  centres  of 
two  pitch  circles,  in  contact  at  T,  and  let  the  circle  A  also  be  the 
describing  circle,  andj?,  a  position  of  the  generating  point  of  a  pair 
of  tooth  forms.  Circle  A,  attempting  to  roll  within  itself,  will 
have  no  motion,  and  the  resulting  hypocycloid  flank  of  A  will 
be  only  the  point  p.  But  let  the  same  circle  roll  on  the  exterior 
of  B,  and  the  same  point,  p,  will  generate  the  epicycloidal  face, 


B. 

Fio.  42. 


pk,  of  B,  which  will  always  be  in  contact  with  a  linear  pin, 
perpendicular  to  the  paper  at  p,  the  contact  beginning  at  T  and 


130  ELEMENTS    OF 

continuing  to  the  left,  motion  being  in  that  direction,  as 
shown. 

Complete  teeth  being  thus  formed,  B  would  drive  A  in  either 
direction. 

Were  A  to  drive  B,  the  pin  p  would  push  against  the  face  pk 
during  the  arc  of  approach  towards  T. 

If,  as  in  the  practical  case,  the  pins  of  the  pin  wheel  are  of 
sensible  diameter,  as  at  P,  the  face  curve,  PK,  of  the  teeth  of  B 
will  be  within  the  former  one,  K',  and  normally  equidistant  from 
it  by  the  radius  of  the  pin  P. 

It  is  found  in  practice,  that  the  friction  during  the  arc  of 
approach  is  more  injurious  than  during  the  arc  of  recession. 
Hence  the  pin  wheel  is  usually  the  follower. 

2.  Pin-wheel  and  Rack. — Either  may  drive,  and,  by  the 
last  principle,  the  pins  will  be  given,  in  each  case,  to  the  follower. 


Then,  first,  let  the  rack  be  the  driver.  The  pitch  circle,  AT, 
will  then  be  also  the  describing  circle  of  wheel  A,  whose  teeth 
will  be  linear  pins,  as  before,  and  the  teeth  curves  of  the  rack 
B  will  be  cycloids,  whose  base  line  is  BT. 

Second :  let  the  wheel  drive.  The  describing  circle  will  then 
coincide  with  the  pitch  line  of  the  rack ;  and  hence  the  tooth 
curves  of  A,  being  generated  by  the  rolling  of  BT  upon  the 
pitch  circle,  will  be  involutes. 

In  each  case,  the  tooth  curve  corresponding  to  a  pin  of  sensi- 
ble diameter  could  be  obtained  as  before ;  but  in  the  last  case 
the  derived  involute  would  be  identical  in  form  with  the  primi- 
tive one. 

3.  Annular  Pin-wheels. — It  is  readily  obvious,  that  if  the 
annular  wheel  drive,  its  teeth  curves  will  be  hypocycloidal.  If 


MACHINE   CONSTRUCTION   AND   DRAWING.  131 

the  annular  wheel  be  a  follower,  the  tooth  curve  of  the  other 
wheel  will  be  the  internal  epicycloid  generated  by  rolling  the 
concave  side  of  the  pitch  circle  of  the  annular  wheel  upon  the 
convex  side  of  that  of  the  driver.  The  final  curves  in  every 
case  being  at  a  normal  distance  from  the  primitive  ones,  equal 
to  the  radius  of  the  pin. 

In  every  case,  of  course,  the  rim  of  the  wheel,  or  rack,  must  be 
hollowed  out  between  the  teeth,  to  allow  of  the  passage  of  the 
pins. 

IV. — Solution  ly  Involute  Teeth. 

1.  Spur-wheels. — These  have  been  mostly  explained  already 
(Theor.  XV.).     It  need  only  be  recalled  here  that  outlines  of 
involute  teeth  consist  of  only  a  single  curve,  instead  of  a  sepa- 
rate face  and  flank,  uniting  at  the  pitch  circle.     These  teeth  are 
also  stronger  than  others,  being  wider  at  the  base.     They  also 
possess  the  valuable  property  of  allowing  the  same  wheels  to 
work  together  with  a  constant  velocity  ratio,  though  the  distance 
between  their  centres  be  changed.     This  arises  from  the  facts 
that  all  involutes  of  the  same  circle  are  equal  curves,  and  the 
lose  circles  may  be  constant  while  the  pitch  circles  change ; 
and  that  the  common  generatrix  of  both  involutes  which  are  in 
contact,  is  the  same  point  on  the  same  line,  which  rolls  succes- 
sively on  the  constant  base  circles.     This  may  be  easily  made 
perfectly  evident  by  a  figure  similar  to  PL  XVIII.,  Fig.  11, 
only  in  which  the  distance  AB  shall  be  changed. 

Since,  however,  the  pressure  between  involute  teeth  is  always 
in  the  direction  of  the  generatrix,  EN,  that  being  their  common 
normal,  a  component  of  this  pressure  will  act  in  the  direction 
of  the  line  of  centres ;  while  in  other  forms  of  teeth  their  pres- 
sure, where  most  effective,  that  is,  in  passing  the  line  of  centres, 
is  perpendicular  to  that  line. 

Involute  teeth  are  therefore  considered  less  advantageous  for 
the  transmission  of  great  pressure  than  for  th-3  transmission  of 
motion,  for  which  they  are  especially  adapted. 

2.  Spur-wheel  and  Raclc. — Let  AT  be  the  pitch  circle,  Fig. 
44,  of  the  wheel,  and  AC  its  base  circle.     Let  BT  be  the  pitch 
line  of  the  rack,  and  IlTn,  tangent  to  AC,  the  generating  line. 
Then  the  involute,  IIK,  will  be  one  of  the  tooth  curves  of  A, 


132 


ELEMENTS    OF 


The  base  circle  of  the  rack  is  at  once  concentric  with  BT,  and 
tangent  to  HT.     That  is,  it  is  infinite,  and  its  contact  with  HT 


is  at  an  infinite  distance  from  T.  Hence,  when  TLTn  rolls  upon 
this  base  circle,  any  point,  as  H,  will  merely  describe  a  recti- 
linear involute,  as  Hm,  perpendicular  to  HT,  which  will  there- 
fore be  the  form  of  the  side  of  the  rack  teeth. 

Since  the  rack  moves  in  the  direction  BT,  while  the  contact 
of  the  teeth  is  on  HT,  the  contact  of  the  teeth  will  not  be  at  a 
single  point  as  in  the  second  solution  (II.). 


EXAMPLE  XXXI. 

To  construct  the  Projections  of  a  Spur-  Wheel,  seen  first  per- 
pendicularly and  then  obliquely. 

After  the  preceding  explanation  of  general  principles,  PI. 
XIX.  may  serve  as  a  full  example  of  the  operations  of  drawing 
a  spur-wheel.  It  may  be  asked  :  why  make  an  oblique  eleva- 
tion? Fig.  2.  It  would  not  be  necessary  in  case  of  a  single 
wheel,  but  some  of  the  different  wheels  of  a  machine  may 
sometimes  be  in  planes  which  are  oblique  to  each  other.  Hence 
the  draftsman  should  by  all  means  be  competent  to  make  any 
oblique  view  of  a  spur-wheel,  or  of  any  other  part  of  a  machine. 

PL  XIX.  represents  a  spur-wheel  of  28  teeth  and  a  pitch  of 
2£  inches. 

Then  the  radius  of  the  pitch-circle  will  be  — 


2jx28  = 
fer 


inches. 


MACHINE   CONSTRUCTION  AND   DRAWING.  133 

Let  the  scale  be  from  2  to  2^  inches  to  the  foot,  according  to 
the  convenience  of  the  student ;  or,  from  one-fifth  to  one-sixth 
of  an  inch  to  an  inch. 

On  some  accounts,  as  in  taking  off  unusual  fractions  of  the 
inch  more  exactly,  it  may  be  better  to  construct  a  diagonal 
scale  of  feet,  inches,  and  8ths  of  inches. 

The  scale  of  the  plate  is  2|-  inches  to  the  foot. 

Description  and  Construction  of  the  Circles  of  the  Wheel. — 
C'a',  Fig.  1,  is  the  radius,  2£  ins.,  of  the  inner  circle  of  the  hub. 
C'b'  is  the  radius,  4^  ins.,  of  the  outer  circle  of  the  hub  at  its 
end,  and  is  seen  in  plan,  Fig.  2,  at  C"b.  C'c'  is  the  radius,  4f 
ins.,  of  the  outer  circumference  of  the  hub,  =  B"c  in  Fig.  2. 

The  circle  of  radius  C'c',  or,  simply,  the  circle  C'c',  is  also 
the  projection  of  the  circle  of  junction, d"H",  Fig.  2,  of  the  hub 
with  the  feather,  or  rib,  which  connects  the  hub,  arms,  and  rim 
together.  C'ef,  5f  ins.,  is  the  outer  radius  of  this  rib,  where  it 
surrounds  the  hub,  that  is,  of  the  two  circles  containing  the 
points  I"  and  K",  Fig.  2.  Likewise  G'g'  is  the  radius,  8f  ins., 
of  the  edges  of  that  part  of  the  rib  which  is  attached  to  the 
under  or  inner  side  of  the  rim.  These  edges  contain  the  points 
T"  and  P',  Fig.  2,  and  lie  in  the  planes  gg  and  M,  Fig.  2,  plan. 
C'i'  is  the  inner  radius,  9  ins.,  of  the  rim,  also  of  the  circle  jj, 
in  Fig.  2,  and  through  U",  Fig.  2,  elevation,  where  the  rib 
joins  the  inner  surface  of  the  rim.  Finally,  CT,  11.14  ins.,  = 
Hi  very  nearly,  is  the  radius  of  the  pitch-circle.  The  other 
radii  are  found  by  construction. 

In  making  the  drawing,  a  tooth  may  have  any  position  rela- 
tive to  the  vertical  centre  line  US  ;  but,  if  bisected  by  that  line, 
as  in  the  figure,  the  equidistant  teeth  011  each  side  will  be  on 
the  same  level ;  which  will  much  lessen  the  labor  of  making 
Fig.  2. 

It  is  only  strictly  necessary  to  make  one  quadrant,  as  XS,  of 
Fig.  1,  and  half  of  either  plan,  since  M"Y  is  an  axis  of  sym- 
metry of  Fig.  2,  EL,  the  portion  above  and  below  being  just 
alike,  while  the  vertical  diameters  of  the  several  circles  of  the 
wheel,  above  described,  and  projected  up  from  C",B",A". 
D'^D'^A"",  etc.,  divide  the  projections  of  those  circles,  in 
Fig.  2,  symmetrically ;  so  that,  for  example,  the  point  on  the 
left  side  of  the  wheel,  corresponding  to  Q"  on  the  right,  would 
be  as  far  to  the  left  of  the  vertical  diameter  through  D",  D'"  as 


164:  ELEMENTS   OF 

Q"  is  to  the  right  of  that  diameter.  But  it  will  be  more  ele- 
mentary and  easy  for  the  learner  to  employ  the  whole  plan ; 
though  either  upper  quarter  of  Fig.  1,  EL,  is  sufficient. 

With  the  scale  and  size  of  plate  here  shown,  take  C',  not  over 
13^  ins.  by  the  scale  from  the  top  and  left-hand  borders,  and 
then  draw,  very  finely  and  accurately,  the  circles  above  de- 
scribed. 

Divide  the  quarter  pitch-circle,  I'l",  into  seven  equal  parts  ; 
or,  to  avoid  puncturing  this  quadrant  by  repeated  trials,  make 
the  division  on  any  exterior  and  concentric  quadrant ;  and  draw 
segments  of  radii,  very  fine,  through  the  points  of  division. 

Take  one  of  these  divisions  of  I'l"  as  a  scale  of  pitch,  and 
divide  it  into  15  equal  parts ;  first  into  five  equal  parts,  and 
then  each  fifth  into  three  equal  parts,  all  very  exactly. 

Let  the  width  of  a  tooth  on  the  pitch-circle,  as  at  I",  be  ^  of 
the  pitch,  and  the  space  between  the  teeth  the  remaining  T8--. 
Then,  on  each  side  of  each  point  of  division  of  the  pitch-circle, 
as  I'J"/",  lay  off  Si-fifteenths  of  the  pitch  ;  and  test  the  widths 
of  the  teeth  to  see  that  each  space  is  just  -^  of  the  pitch  scale 
wider  than  a  tooth.  Or  the  whole  pitch  may  be  set  off  succes- 
sively, on  the  pitch-circle,  from  each  side  of  the  tooth  I'  towards 
the  one  at  I",  or  from  I",  likewise,  towards  the  tooth  I'.  Thus 
all  the  pitch-circle  points  will  be  located. 

For  mere  purposes  of  graphical  construction,  the  faces,  as  v 
and  v',  of  the  teeth  may  be  circular  arcs,  whose  radius  is  the 
pitch,  and  whose  centres  are  on  the  pitch-circle.  These  arcs 
extend  from  the  pitch-circle  points,  just  found,  to  the  point- 
circle,  which  is  thus  found.  The  extent  of  the  teeth,  beyond 
the  pitch-circle,  is  5^-fifteenths  of  the  pitch.  Then  make  I'm' 
equal  to  5^-fifteenths  of  the  pitch,  and  draw  a  new  circle 
through  ra'j  with  C'  as  a  centre,  for  the  outer  limit  of  the  faces, 
as  w'w" . 

The  flanks,  as  w'y'",  are  here  radial  lines,  whose  inner  limit  is 
the  root-circle,  C'k' /  found  by  making  I'Jc'  equal  to  6^-fifteenths 
of  the  pitch. 

At  this  stage  of  the  construction,  the  entire  rim,  with  the 
circles  of  the  hub,  making  the  key-seat  of  any  suitable  size,  may 
be  inked,  observing  the  obvious  position  of  the  heavy  lines. 

This  done,  proceed  with  the  construction  of  the  arms  and 
connecting-rib  as  follows :  Let  the  taper  of  the  arms  be  such 
that,  if  produced  to  the  centre  lines,  XY  and  ES,  they  would 


MACHINE   CONSTRUCTION   AND   DRAWING.  135 

there  be  5  ins.  wide,  and  4  ins.  wide  at  a  distance,  as  C'o,  of  5f 
inches  from  C'. 

The  ribs,  as  R/,  upon  the  arms,  are  uniformly  1J  in.  thick 
throughout  their  straight  part,  as  seen  in  Fig.  1. 

The  constructions,  as  at  s,  <?,  j9,  and  r,  for  finding  the  centres 
of  the  little  arcs,  by  which  the  several  intersecting  edges  of  the 
wheel  are  rounded  into  each  other,  mostly  explain  themselves. 
It  is  only  necessary  to  notice  that  the  short  portions,  as  ut',  of 
an  arc  which  is  rounded  into  a  straight  line,  as  un',  are  treated 
as  straight ;  t's  is  then  a  radial  line,  and  ts  is  perpendicular 
to  un'j  and  ut'  and  ut  are  equal.  The  other  constructions  are 
similar. 

Construction  of  the  Plans. — Only  one  finished  plan,  Fig.  2, 
is  necessary.  To  make  it,  project  down  all  the  necessary  points 
of  each  circle  in  the  elevation  of  Fig.  1,  separately,  upon  sep- 
arate lines,  parallel  to  XY.  Then  construct  the  outlines  of 
Fig.  2,  plan,  by  the  following  measurements:  The  face  of  the 
wheel,  as  at  Mm,  is  6f  ins.  wide.  Then,  first,  locate  the  rec- 
tangle Mmm",  far  enough  to  the  right  to  separate  Figs.  1  and 
2,  suitably,  and  make  its  width  6f  ins.,  and  its  length  equal  to 
twice  C'm'.  Draw  its  transverse  centreline,  C"A"",  and  make 
the  hub  plan  8f  ins.  for  the  extreme  length,  and  7f  ins.  for  the 
length  of  the  thicker  portion  GG'". 

Construction  of  the  Oblique  Elevation. — E very  point  of  this 
is  found  by  the  elementary  operation  shown  in  Fig.  11 ;  on  the 
one  principle  that  each  point,  as  m",  is  on  a  perpendicular,  mm", 
to  the  ground  line  from  the  plan,  m-,  of  that  point,  and  at  its  in- 
tersection with  the  parallel,  m'm",  from  the  primitive  elevation, 
m',  of  the.  same  point. 

Where  many  separate  groups  of  points  are  to  be  constructed, 
and  each  group  to  be  shown  in  separate  projections,  it  is  of 
prime  importance,  in  order  to  secure  ease  and  accuracy,  and  to 
avoid  confusion,  to  construct  each  group  separately,  and  in  Fig. 
2,  Elev.,  where  each  point  is  found  from  Figs.  1  and  2,  plan, 
the  whole  construction  for  each  point  should  be  complete  before 
beginning  that  of  a  new  point. 

To  illustrate,  let  us  take  the  outermost  ring  of  points  m"S"Y. 

Draw  any  line  parallel  to  X  Y,  below  Fig.  1,  Elev.,  and  upon 
it  project  down  0',  and  all  the  points  of  the  point  circle  m'S, 


136  ELEMENTS   OF 

only.  Then  transfer  these  points  carefully  to  mm'" ,  Fig.  2,  by 
the  dividers,  or  by  a  slip  of  paper  having  these  points  exactly 
marked  on  its  edge.  Then  draw  the  point  lines  of  the  teeth, 
as  1 — 1 ;  2 — 2,  etc.  Then  project  up  all  the  points  as  1,  on 
mm'",  one  at  a,  time,  and  project  over  the  same  points,  as  w", 
from  Fig.  1.  The  intersection  of  these  projecting  lines  will  give 
1',  etc.,  on  the  oblique  elevation,  Fig.  2.  In  the  same  way  find 
all  the  points  of  the  point  circle,  m'S — mm!" — m"S".  Then 
take  a  new  line  below  Fig.  1,  Elev.,  and  parallel  to  XY,  and  go 
through  a  similar  round  of  operations  for  finding  the  pitch 
circle  points.  In  like  manner,  also,  every  point  of  Fig.  2,  Elev., 
is  found.  It  is  only  necessary  to  transfer  the  horizontal  projec- 
tions of  the  different  circles  of  Fig.  1,  each  to  its  proper  plane 
in  Fig.  2,  plan.  Thus,  l)y  is  the  plane  of  the  circles  C'a'  and 
C'b',  of  Fig.  1.  B"c  is  that  of  G'c',  Fig.  1.  The  latter  circle  is 
also  laid  off  from  D"  as  centre,  in  gg,  in  Fig.  2,  plan,  to  give 
the  intersection,  through  H",  Fig.  2,  Elev.,  of  the  hub  with  the 
rib.  This  rib  is  shown  in  plan,  Fig.  2,  by  the  dotted  lines  gg 
and  hh,  1£  in.  apart.  Then  the  circles  G'e'  and  C'</'  are  both 
laid  off,  both  on  gg  arid  hh,  to  give  the  front  and  back  edges, 
through  I"  and  K",  and  through  T"  and  Q",  of  the  visible 
parts  of  the  rib.  C'i'  is  laid  off  on  mm'"  for  the  front  circle, 
i"i",  of  the  rim ;  on  jj,  for  the  intersection  of  the  web  and 
rim,  and  on  MP'",  for  the  back  circle  through  P',  of  the  rim. 

The  horizontal  arms  which  are  only  seen  edgewise  in  elevation, 
Fig.  1,  are  seen  flatwise  in  plan,  and  are  thus  drawn  :  At  their 
junction,  as  s"s'",  with  the  hub,  they  are  6f  ins.  wide.  They 
taper  from  a  width  of  6f  ins.,  if  produced  to  the  axis,  as  at 
A" A"',  to  a  width  of  4f  ins.,  at  the  distance  of  8f  ins.  from 
the  axis.  Their  extremities  are  rounded  as  shown  in  Fig.  2, 
plan.  To  find  their  oblique  elevations,  use  their  principal  points, 
on  Figs.  1,  Elev.,  and  2,  plan,  that  is,  such  points  as  t  and  L, 
where  their  straight  and  curved  edges  join. 

Further  directions  might  only  confuse  the  subject.  By  fully 
understanding  from  the  foregoing  how  any  one  point  of  Fig. 
2,  Elev.,  is  found,  all  can  be  found,  since  all  are  constructed  in 
the  same  way. 

"We  only  add  some  ways  of  checking  the  work.  First.  If 
lines  pass  through  a  point  in  space,  their  projections,  on  any 
plane,  will  contain  the  similar  projection  of  that  point.  Hence 


MACHINE   CONSTRUCTION   AND   DRAWING.  137 

all  the  flanks  on  Fig.  2  should  radiate  from  A"',  the  projection 
of  C',A",  the  centre  of  the  face  of  the  wheel.  Second.  Each 
circle  of  the  wheel  will  be  vertically  projected  on  Fig.  2,  in  an 
ellipse,  which  can  be  readily  found,  by  construction  from  its 
axes,  as  in  (26,  27),  and  then  points  of  these  circles,  as  OO",  or 
NN",  can  be  projected  up  from  Fig.  2,  plan,  or  over  from  Fig.  1, 
Elev.,  upon  these  ellipses.  Portions  of  the  curved  edges  of  the 
web  were  thus  found  in  Fig.  2,  as  that  through  e',e,e".  Com- 
pare also  corresponding  radii,  as  D'"H",  which  is  the  same  line 
as  the  radius  C'G',  Fig.  1.  Third.  The  thickness  of  the  rib 
being  everywhere  the  same,  the  lines  gh,  ef,  IK,  etc.,  Fig.  2, 
plan,  are  parallel,  hence  their  vertical  projections,  as  I"K",  or 
Q"T",  are  of  constant  length.  That  is,  having  any  front  circle, 
the  points  of  the  corresponding  back  circle,  in  Fig.  2,  Elev.,  are 
found  by  laying  off  a  constant  horizontal  distance  from  its 
front  points.  Thus  the  back  points,  M",O",  etc.,  of  the  teeth, 
so  far  as  visible,  are  found  by  laying  off  the  constant  dis- 
tance, M' W,  from  their  front  points.  In  like  manner  P'  is 
found  from  P".  Also,  G"II",  the  vertical  projection  of  GH, 
is  constant ;  as  so  is  P"U",  the  vertical  projection  of  PU. 

100.  Introductory  to  the  next  example,  we  will  here  explain 
more  in  detail  than  hitherto  the  formation  of  a  bevel  wheel. 

Let  Y,  PI.  XX.,  Fig.  7,  be  the  common  vertex  of  a  pair  of 
bevel  wheels,  and  YJ  the  generatrix  of  the  primitive  cone  from 
a  frustum  of  which  the  wheel  is  formed,  and  let  YY"  be  the 
axis  of  this  cone  and  of  the  wheel.  This  cone  will  then  be  the 
pitch  cone  of  the  wheel.  Let  Yc?  be  the  generatrix  of  the  point 
cone  j  and  Y/*,  that  of  the  root  cone.  Let  the  ends  of  the  teeth, 
whose  length  is  bo,  be  conical  surfaces,  normal  to  the  pitch 
cone.  Then  dV"  and  n~V'  are  the  generatrices,  and  Y"  and  Y' 
the  vertices  of  these  cones.  Now  let  the  five  generatrices,  thus 
far  described,  revolve  about  the  common  axis  YY".  The 
points  d,  b  and  f  will  respectively  generate  the  outer  point, 
pitch,  and  root  circles  ;  and  n,  o  and  p  will  generate  the  inner 
point,  pitch,  and  root  circles ;  and  all  of  these  circles  will  be 
perpendicular  to  the  common  axis  YY". 


138  ELEMENTS   OF 

EXAMPLE  XXXII. 

To  construct  ike  Projections  of  a,  Bevel   Wheel  whose  axis 
is  perpendicular  to  the  vertical  plane. 

Let  VY" — O'  be  the  axis  of  the  wheel ;  let  the  following  be 
its  measurements,  laid  off  to  a  scale  of  2£  inches  to  1  foot,  = 
fV  of  an  inch  to  1  inch,  or  of  \  or  \  of  an  inch  to  1  inch,  as 
may  be  most  convenient.  Make  V#  =  IGf  inches,  and  db  = 
am  =  llf  inches,  and  draw  5V  for  the  extreme  element  of  the 
pitch  coiie.  tnb  is  then  the  horizontal  projection  of  the  outer 
or  greater  pitch  circle.  Draw  5V"  perpendicular  to  5V,  and 
5V"  will  be  the  extreme  or  horizontal  element  of  the  cone  con- 
taining the  outer  or  larger  ends  of  the  teeth. 

With  centre  V"  and  radius  V"5  draw  an  arc  50,  which  will  be 
the  development  of  a  portion  of  the  pitch  circle,  mb,  consider- 
ed as  the  base  of  the  cone  V"ra5. 

With  centre,  O',  and  radius,  O'5'  =  ab,  draw  the  vertical  pro- 
jection, ni'u'l)' ',  of  the  outer  pitch  circle,  and  divide  each  quad- 
rant of  it  into  five  equal  parts,  to  obtain  the  pitch  ;  since  the 
wheel  is  supposed  to  have  20  teeth.  Lay  off  this  pitch,  which 
by  measurement  is  3f  inches,  once,  011  50,  from  5,  which  will 
give  the  point  B. 

Adopting  the  finer  proportions  given  in  (95),  divide  5B  into 
fifteen  equal  parts,  and  lay  off  seven  of  these  parts  from  5  and 
B,  to  give  the  widths  of  the  teeth  5  A  and  BO.  Xext,  lay  off 
bd  —  5£  of  these  fifteenths,  to  give  d,  a  point  on  the  point  circle 
dF.  Also  6^-fifteenths  from  b  tof,  giving/*,  a  point  of  the  root 
circle  /D.  Make  fh  —  ij  inches,  for  the  thickness  of  the 
conical 'rim  which  bears  the  teeth,  and  draw  the  arc,  AE,  of  the 
development. 

We  now  have  this  set  of  four  parallels  to  the  ground  line, 
viz. :  dd",  the  outer  point  circle ;  bm,  the  outer  pitch  circle  ; 
ff",  the  outer  root  circle ;  and  M",  the  outer  rim  circle.  Pro- 
ject up  the  three  foremost  of  these,  only,  since  the  rim  circle 
is  hidden  in  vertical  projection  by  the  rim  itself,  giving  the 
point  circle,  O'd' ;  the  pitch  circle,  O'5',  already  projected,  and 
O'fj  the  root  circle. 

Returning  to  the  plan,  draw  dV,  f^i  an<^  ^"^"j  and  on  ^ 
make  bo  =  4%  inches,  for  the  length  of  a  tooth.  Then  draw 
Von,  parallel  to  V"5,  for  the  extreme  element  of  the  cone 


MACHINE   CONSTRUCTION   AND   DRAWING.  139 

containing  the  inner  ends  of  the  teeth.  The  intersections  of 
this  line,  with  those  already  drawn  to  V,  will  be  the  extremi- 
ties of  the  inner  point  circle,  nG  ;  the  inner  pitch  circle,  0H ; 
the  inner  root  circle,  pi ;  and  the  inner  rim  circle,  qK.  The 
vertical  plane  face,  ^K,  of  the  wheel,  is,  however,  rounded  into 
the  cone  of  the  inner  ends  of  the  teeth  by  a  concave  double 
curved  surface,  as  indicated  by  the  curve  at  qp.  Hence  pro- 
ject up  only  the  three  foremost  circles,  giving  the  inner  circles, 
Ojp',  O'o',  and  O'n':- 

Now,  each  point  of  division,  as  y,  made  in  finding  the  pitch, 
is  the  middle  point  of  a  tooth,  on  the  outer  pitch  circle,  in  or- 
der that,  for  convenience,  the  vertical  line,  O'Y",  shall  be  an 
axis  of  symmetry  of  the  vertical  projection.  Then  make 
•y£'  =.  yu'  =  \  &A,  the  width  of  the  tooth  in  development,  and 
do  the  same  at  each  other  similar  point  of  division.  Also,  for 
each  tooth  make  the  point  at  s,  where  the  outer  point  circle  is  cut 
by  the  radius,  as  O'y,  and  make  sM?=  sv'=  £FF",  the  width  of  a 
tooth  at  the  point.  Since  the  development  shows  the  true  form 
of  the  ends  of  the  teeth,  the  curves,  as  M'N7  and  u'v,  may  be 
drawn  with  sufficient  accuracy,  as  circular  arcs  with  their  centres 
found  by  trial  on  the  pitch  circle  m'u'b,  taking  care  that  all  of 
them  shall  have  the  same  radius. 

The  flanks  of  the  teeth  being  radial  plane  surfaces,  as  indi- 
cated in  the  development,  their  planes  will  all  contain  the  axis 
YY" — O',  and  hence  their  vertical  projections  will  simpry  be 
the  straight  lines,  as  u'S',  limited  by  the  inner  root  circle  O'p', 
and  converging  to  O'.  Add  the  point  lines,  as  M'Q',  also  con- 
verging to  O',  and  the  inner  face  curves,  as  Q't",  drawn  as  M'N' 
was,  that  is,  with  centres  now  on  the  inner  pitch  circle  O'o',  and 
the  vertical  projection  of  the  teeth  will  be  complete.  To  find 
the  elevation,  only  draw  the  eye  of  the  wheel  with  a  'radius  O'r' 
of  3f '.  \lr'  is  the  key  seat,  of  any  suitable  size. 

Before  constructing  the  plan,  it  must  be  understood  that  it 
represents  the  wheel  with  the  upper  right-hand  quadrant  cut 
out ;  so  that  the  part  to  the  right  of  YY"  shows  the  lower 
right-hand  quarter,  not  seen  in  the  elevation,  and  a  section  in 
the  horizontal  plane  O'd'. 

This  being  understood,  project  down  the  outer  points,  as  H' 
and  v',  of  the  left-hand  half  of  the  elevation,  upon  the  outer 
point  circle  dd" ,  as  at  M  and  v,  and  through  these  points 
draw  the  point  lines,  as  MQ,  towards  Y.  Project  down  the 


14:0  ELEMENTS    OF 

pitch  points,  as  X'  and  u,  upon  the  outer  pitch  circle,  Jwi,  and 
draw  the  outer  flank  lines,  as  NP,  towards  V",  giving  the  root 
point,  as  P  and  R.  Thence  draw  the  visible  root  lines,  as  RS, 
towards  Y,  and  limited  by  the  inner  root  circle  jpi.  Having 
gone  thus  far,  the  inner  pitch  points,  as  t,  may  be  found  in 
three  ways  :  first,  by  projecting  down  from  their  elevations,  as 
t ;  second,  by  drawing  the  inner  flank  lines,  as  Stf,  radiating 
from  Y' ;  third,  by  making  the  intersections  of  the  imaginary  pitch 
lines,  as  ut,  drawn  towards  Y,  with  the  inner  pitch  circle,  6»H. 

As  the  teeth  are  seen  under  various  angles,  no  two  on  the 
same  quarter  of  the  wheel  will  appear  alike,  and  the  face 
curves,  as  NM,  must  be  sketched  by  hand. 

As  the  teeth  on  the  right-hand  lower  quarter  are  vertically 
under  those  of  the  right-hand  upper  quarter,  the  latter  will 
serve  equally  well  for  purposes  of  projection.  Thus,  project 
down  the  points,  asT',  of  the  inner  ends  of  the  teeth  to  find  T, 
etc.,  on  the  inner  point  circle.  Likewise  project  down  the 
inner  points,  as  U',  to  find  U,  etc.,  on  the  inner  pitch  circle,  oYL. 
Then  draw  the  face  curves  by  hand ;  and  the  flank  lines,  as 
UU",  radiating  towards  Y' ;  and  the  visible  portions,  as  TT", 
of  point  lines,  radiating  from  Y. 

To  complete  the  plan,  make  the  length,  K*,  of  the  hub =6 
inches;  its  greater  radius,  7^,  6f  inches,  {&  =  %  an  inch,  and  the 
radius  at  ij  =  6£  inches. 

The  portion  rr"pfhj,  is  the  generatrix  of  the  united  hub  and 
rim,  by  revolving  about  the  axis  YY".  The  rim  is  further 
bound  to  the  hub  by  four  arms,  which  bridge  the  annular  open 
space  generated  by  l"f"h.  These  arms  are  2  inches  wide, 
therefore  make  Ttk"  =  1  inch  ;  Ik"  and  l"h  are  edges  of  arms; 
and  l"w,  a  minute  distance,  strictly,  to  the  right  of  I,  is  the 
intersection  of  the  side  of  the  arm  with  the  cylindrical  surface 
of  the  hub.  It  can  be  constructed  by  projecting  down  from  a 
fragment  of  the  hub  and  horizontal  arm,  easily  made  in  verti- 
cal projection. 

EXAMPLE  XXXIII. 

To  construct  the  Projections  of  a  Bevel  Wheel,  seen  obliquely 
relative  to  the  vertical  plane. 

See  PI.  XX.,  Fig.  2,  where  like  points  have  the  same  letter 
in  both  projections,  and  on  Fig.  1. 


MACHINE   CONSTRUCTION   AND   DRAWING.  141 

Begin  with  the  plan,  which  is  simply  a  copy  of  that  in  Fig.  1, 
except  in  being  in  a  different  position  relative  to  the  ground  line, 
and  in  showing  the  parts  on  both  sides  of  Y V"  alike.  YY"  is 
thus  an  axis  of  symmetry  from  which  the  various  points  on  the 
several  circles  of  the  wheel  are  laid  off,  each  way,  on  On,  ott 
j)S,  ab,  etc.,  which  are  at  the  same  distance  apart,  and  from  Y, 
as  are  the  same  lines  in  Fig.  1. 

The  plan  being  thus  simply  made,  the  elevation  may  be  made 
wholly,  or  in  part,  in  any  one  of  three  ways,  but  best  by  a  com- 
bination of  any  two  of  them ;  either  serving  as  a  check  upon  the 
other,  and  some  points  being  found  best  by  one  method,  and 
some  by  another,  according  to  their  positions ;  having  regard  to 
the  principle  that  the  lines  of  construction,  which  determine 
any  point,  should  form  as  large  an  angle  as  possible  with  each 
other.  % 

First  Method. — Every  point  of  the  elevation  may  be  found 
by  the  elementary  operation  of  projecting  up  the  points  of  the 
plan,  as  P,  into  horizontal  projecting  lines,  as  p'p',  from 'the 
same  point  on  the  elevation  in  Fig.  1.  In  this  case,  the  lines  of 
construction  will  always  meet  at  right  angles ;  but  two  things 
must  be  noticed :  first,  to  avoid  confusion,  only  one  point  at  a 
time,  as  MM',  for  example,  should  be  projected  up,  and  pro- 
jected over  from  the  elevation,  Fig.  1.  It  is  a  bad  practice 
to  draw  a  great  number  of  projecting  lines  from  the  plan, 
and  then  a  great  many  from  the  elevation,  Fig.  1,  before 
noting  any  of  their  intersections.  Second,  by  this  method 
quite  a  number  of  invisible  points  of  the  inner  ends  of 
the  teeth  must  be  marked  on  the  plan;  by  finding  them 
first  on  the  plan,  Fig.  1,  by  projecting  down  from  the  eleva- 
tion. 

Second  Method. — By  any  of  the  familiar  methods,  construct 
(26-27)  the  six  ellipses,  as  m'Wb'  and  G'TV,  in  the  elevation, 
which  will  be  the  vertical  projections  of  the  six  visible  tooth- 
circles  of  the  wheel.  Thus  the  semi-ellipse  m'Wb'  has  for  its 
semi-transverse  axis  K'Y"  =  ab,  and  for  its  conjugate  axis  m'b', 
the  vertical  projection  of  mb.  After  constructing  these  ellipses, 
the  points  of  the  teeth  found  upon  them,  as  M',N',P',T",U',S', 
may  be  conveniently  projected  up  from  the  plan,  for  the  teeth 
near  the  highest  one  ;  and  over  from  the  elevation,  Fig.  1,  for 
those  near  the  ground  line.  And  the  points  thus  constructed 
should  be  joined  as  fast  as  found. 


142  ELEMENTS   OF 

Third  Method. — After  constructing  any  two  rings  of  points, 
but  preferably  those  of  the  larger  ends  of  the  teeth,  by  the  first 
or  second  method,  all  the  remaining  points  can  be  found  by 
projecting  them  from  the  plan,  or  from  the  elevation  in  Fig.  1, 
upon  the  lines  meeting  at  O',  O",  and  O'".  For  these  points 
are  the  vertical  projections  of  the  three  vertices,  Y,  V,  and  V", 
to  one  or  another  of  which  every  straight  line  of  the  wheel 
tends. 

Thus,  having  found  M'  and  'N',  for  example,  by  the  first 
method,  Q'  will  be  the  intersection  of  M'O',  with  a  projecting 
line  from  Q,  or  from  Q',  in  Fig.  1. 

By  this  method,  certain  invisible  points  of  the  elevation  must 
be  temporarily  found.  Thus,  find  the  invisible  back  root  point, 
P",  and  then  S'  will  be  the  intersection  of  ?"()',  with  a  project- 
ing line  from  S,  or  from  S'  in  Fig.  1. 

But  some  of  the  points  may  be  found  by  the  intersections  of 
these  converging  lines  with  each  other.  Thus,  having  found 
S'"  as  before,  t"  will  be  the  intersection  of  O"S"',  produced, 
with  N'O'.  Or,  better,  finding  t"  first,  S'"  will  be  the  intersec- 
tion of  P'O'  and  t"Q". 

Fourth  Method. — This  merely  consists  in  applying  the  prin- 
ciple, in  connection  with  the  other  methods,  that  for  the  same 
side  of  the  same  tooth,  lines  as  O'/rN"'  and  O"t"  are  parallel. 
Thus,  having  N'O'"  and  IsPO',  the  point  t"  maybe  found  as  the 
intersection  of  O"t",  parallel  to  O'"W,  with  N'O'. 

101.  To  construct  the  oblique  projection  of  the  foregoing,  or 
any  other  object,  by  using  only  three  projections,  proceed  as 
illustrated  for  a  semicircle  only,  in  PL  XX.,  Fig.  3.     Then  let 
AB  be  the  horizontal  projection  of  a  vertical  semicircle.     Let 
a'b'  be  the  ground  line  of  an  auxiliary  vertical  plane,  parallel  to 
the  plane  of  the  semicircle,  and  on  which  the  latter  will  there- 
fore be  shown  in  its  true  size,  as  at  a'e'b'.     Let  A'B'  be  the 
ground  line  of  a  vertical  plane  oblique  to  the  semicircle,  and 
on  which  the  required  projection  is  to  be  found.     To  do  this,  it 
is  only  necessary  to  project  up  the  several  points,  A,  C,  E,  etc., 
of  the  plan,  and  make  their  heights,  M'C',  O'E',  etc.,  equal 
to  m'c',  o'e',  etc.,  on  the  principle  that  the  different  vertical 
projections  of  the  same  point  are  at  the  same  height  above  their 
respective  ground  lines. 

102.  Minor  modifications  of  the  construction  just  given  are 


MACHINE   CONSTRUCTION   AND   DRAWING.  143 

obvious.  Thus,  AB  might  have  been  parallel  to  the  plane  A'B', 
and  then  the  oblique  elevation  would  have  been  at  a'e'V. 
Again,  the  plane  A'B'  might  have  been  made  parallel  to  AB, 
and  the  plane  a'b'  parallel  to  the  present  direction  of  A'B',  in 
which  case,  again,  the  highest  of  the  three  figures  would  have 
been  the  oblique  elevation.  Finally,  let  a'V  be  brought  down 
parallel  to  itself,  near  to  AB ;  let  A'B'  be  carried  up  parallel  to 
itself ;  and  then  let  AB  be  placed  parallel  to  the  present  posi- 
tion of  A'B' ;  and  then  the  middle  figure  will  be  the  oblique 
projection. 

Practical  Forms  of  the  Teeth  of  Wheels. 

103.  After  all  the  foregoing   statement  of   only  the  main 
points  in  the  theory  of  the  teeth  of  wheels,  it  must  be  acknow- 
ledged that  in  practice  they  are  bounded  by  circular  arcs.     In 
empirical  practice  these  arcs  are  taken  arbitrarily,  and  even 
absurdly.     In  scientific  practice  they  are  taken  so  as  to  conform 
as  closely  as  possible  to  the  theoretical  outlines. 

104.  The  theory  as  above  given  is  thus  abundantly  useful,  as 
leading  to  the  determination  of  proper  approximate  arcs.   And, 
on  the  other  hand,  the  length  of  an  epicycloidal  or  involute  arc 
forming  the  limits  of  the  side  of  a  tooth  in  a  real  wheel  is  so 
small,  that,  except  for  very  large  wheels,  the  circular  arc,  how- 
ever finely  traced,  would  sensibly  coincide,  except,  perhaps, 
under  a  magnifier,  with  the  theoretical  curves,  within  these 
small  limits. 

A  not  uncommon  empirical  method  for  constructing  the 
faces,  the  flanks  being  radial,  is  to  describe  them  with  the 
pitch  for  a  radius,  and  the  centre  in  the  pitch  circle,  as  in  Ex. 
XXXI. 

105.  Among  scientific  practical  methods,  the  following  are 
the  principal,  if  not  the  only  ones : — 

First :  Construct  templets,  as  T,  Fig.  45,  that  is,  thin  pieces 
of  hard  wood,  carefully  shaped  to  the  exact  curvature  of  the 
intended  pitch  circles  and  describing  circle.  The  latter  of  these 
templets,  C,  carries  in  its  circumference  a  firm,  sharp  tracing- 
point,  JP.  Then,  by  rolling  it  successively  upon  the  pitch  tem- 
plets, the  correct  face  curves  of  teeth  are  traced  mechanically, 
and  by  rolling  it  on  other  templets  of  the  same  curvature,  but 
concave  on  their  curved  edges,  the  flanks  of  the  same  teeth  will 


144 


ELEMENTS   OF 


be  traced ;  in  both  cases  upon  a  board  on  which  the  pitch 
templets  are  held,  so  as  to  coincide  with  the  pitch  circles  traced 
upon  it. 

A  templet  can  then  be  cut  to  the  form  of  the  tooth,  and  used 
in  tracing  the  outlines  of  the  ends  of  the  teeth  on  the  rough 
pattern  of  a  wheel.  • 

A' 


B. 


Second :  Having  traced  a  face  and  a  flank,  as  above,  take 
three  points  on  each,  and  by  the  familiar  method  construct  the 
circular  arc  passing  through  those  three  points,  and  it  will 
approximate  very  closely  to  the  theoretical  curve. 

106.  Both  of  these  methods  would  evidently  be  nearly  or 
quite  impracticable,  except  for  quite  large  teeth ;  while  the 
second  is  rather  vague,  owing  to  the  somewhat  arbitrary  as- 
sumption of  the  three  points.  Besides,  by  the  insensible  slip- 
pings  of  the  templets,  and  minute  instrumental  errors,  the  sup- 
posed true  curve  might  be  more  erroneous  than  a  circular  ap- 
proximation made  from  a  single  centre  by  some  simple  rule. 
Therefore — 

Third  :  Let  the  approximate  circular  arc  be  described  from 
a  mean  centre  and  radius  of  curvature  of  the  theoretical  teeth. 
These  data  can  be  determined  analytically,  and  thus  each  tooth- 
curve  may  be  struck  at  once  with  a  single  centre  and  radius. 
This  method  has  been  proposed  by  Euler  and  Eedtenbacher, 
and  one  adapted  to  practice  was  founded  upon  it  by  Prof. 
Willis  (Principles  of  Mechanism),  and  conveniently  embodied 
in  an  instrument  called  the  odontograph,  the  theory  and  use  of 
which  will  next  be  briefly  described. 


MACHINE   CONSTRUCTION   AND   DRAWING.  145 


THEOREM  XX. 

Circular  tooth-curves,  with  centres  on  a  line  through  the 
point  of  contact  of  the  pitch  circles,  will  gvve  a  sensibly  con- 
stant velocity  ratio  to  those  circles. 


Pis.  46. 

Let  A  and  B,  Fig.  46,  be  the  centres  of  the  pitch  circles, 
whose  contact  is  T.  Through  T  draw  ~Nn,  and  make  TK  =  T&, 
perpendicular  to  ~Nn,  and  less  than  either  pitch  circle  radius. 
Draw  AK  to  N ;  A&,  giving  m;  BK,  giving  M ;  and  B&  to  n* 
Also  draw  BR  perpendicular  to  ~Nn.  Now  conceive  the  system 
Bn  /  nmR ;  Am  to  be  jointed  at  n  and  m,  and  on  the  point  of 
turning  about  the  fixed  centres,  A  and  B.  For  the  instant  of 
occupying  the  position  shown  in  the  figure,  we  have 
nk  :  &T  ::  nB  :  BR. 

But  as  &T  is  a  fixed  line,  this  proportion  simply  shows  that  T, 

alone,  is  the  fixed  point  of  "Nn  for  the  instant,  or,  in  other 

words,  is  the  intersection  of  two  consecutive  positions  of  Nn* 

And,  as  T  is  on  the  line  of  centres  AB,  while  nN  is  a  common 

10 


ELEMENTS    OF 

normal  to  a  pair  of  tooth  curves,  when  their  centres,  as  M  and  N, 
or  m  and  n,  are  on  that  line,  it  follows,  from  Theorem  XVIL, 
that  such  tooth  curves  will  give  a  constant  angular  velocity 
ratio  for  the  instant  in  which  T  is  fixed  as  above  described. 
These  curves  being  quite  short,  this  velocity  ratio  will  be  sen- 
sibly constant  during  the  short  period  in  which  they  are  in 
contact. 

TK  =  T&  is  less  than  either  AT  or  BT,  merely  to  throw  both 
of  a  pair  of  centres,  as  m  and  n,  on  the  same  side  of  the  tooth 
curves  B,  so  that  one  of  the  latter  shall  be  convex  towards  the 
concavity  of  the  other.  Then,  this  being  understood,  the 
remoter  centre  is  that  of  the  concave  tooth  curve,  which,  of 
course,  is  a  flank.  But  each  wheel  must  have  both  faces  and 
flanks.  Hence  for  one  face  and  flank  pair,  acting  together,  the 
wheels  are  momentarily  represented  by  the  linked  arms  Am 
and  Btt  /  giving  m,  the  centre  of  a  face  of  A,  and  n,  the  centre 
for  the  corresponding  flank  of  B.  Conversely,  for  the  other 
pair,  the  wheels  are  represented  momentarily  by  the  arms  AN" 
and  BM ;  giving  M  the  centre  of  a  face  of  B,  and  N  the  centre 
for  the  corresponding  flank  of  A. 

106.  If  we  take  the  contact  of  the  tooth  arcs  a  little  way 
from  T,  on  the  opposite  side  from  m  and  n,  there  will  be  a 
corresponding  pair,  at  the   same  distance  to   the   left  of  T, 
so  that  the  action  will  be  exact  at  two  points  in  the  total  arc 
of  action ;  which  will  give  abundant  accuracy  of  action  at  all 
points. 

107.  Assuming  the  total  arc  of  action  to  be  about  twice  the 
pitch,  in  all  cases,  the  contact  of  the  first  pair  of  tooth  curves 
may  be  at  a  distance  from  T  equal  to  half  the  pitch. 

Finally,  the  angle  nTA.  is  found  experimentally  to  be  best 
fixed  at  75°. 

By  calculating  and  tabulating  the  distances,  as  nT  and  MT, 
for  wheels  of  various  sizes,  and  by  graduating  them  on  the 
odontograph,  PI.  XXI.,  Fig.  2,  the  final  adaptation  of  this  sys- 
tem to  practice  will  be  made. 

These  distances  are  easily  found,  as  follows.* 

*  Willis'  Principles  of  Mechanism,  p.  125. 


MACHINE   CONSTRUCTION   AND   DRAWING.  147 

PROBLEM  VIII. 
To  find  the  Radii  of  the  Tooth  Curves. 

Let  TK  =  a    ;    BT  =     R 
TM  =  c  and  BTR  =  * 

Then  from  the  similar  triangles,  BRM  and  KTM. 
TM:MR  ::  TK  :  BR. 
Whence  TM  x  BR  =  MR  x  TK 
But   MR  =  TR  -  TM ;    BR  =  R  sin  «  and 

TR  =  R  cos  *. 

Hence,  by  substitution,  TM  x  R  sin  *  =  R  cos  *  x  TK  — 
TM  x  TK.' 

Or  TM  (R  sin  «  +  TK)  =  TK  x  R  cos  *. 

•n  v.'   i-  rnir         TK    X    R  COS  * (1.) 

From  which  TM  =  =r77 =-— -. 

TK  -f  R  sin  « 

It  only  remains  to  show  how  the  length  of  TK  should  be 
governed.  Now,  in  every  systematic  manufacture,  a  certain 
series  of  pitches,  and  numbers  of  teeth,  will  be  adopted,  as  suf- 
ficient for  all  ordinary  cases.  The  greatest  pitch  and  number 
of  teeth  will  determine  the  greatest  wheel,  and  the  least  of  both 
elements  will  determine  the  smallest  wheel,  and  by  various 
combinations  of  the  two  elements,  wheels  of  almost  any  inter- 
mediate size  can  be  made,  while  the  radius  can  be  immediately 
found  from  the  formula 

P       P  x  N 

~2^~ 

where  P  —  pitch,    N  =  number  of  teeth,   and    R  =  radius. 
TK,  then,  is  so  taken  that  for  the  least  wheel  of  a  set,  AK  shall 
be  parallel  to  TN,  thus  giving  a  flank  centre  at  an  infinite  dis- 
tance from  T,  and  hence  a  straight  flank  for  the  least  wheel. 
Denote  the  least  radius,  A'T,  by  r,  then 

TK  =  r  sin  «, 
which,  substituted  in  (1),  gives 

TM  -  Rr  cos  *     (2) 

"    R  +  r 

In  like  manner,  beginning  with  the  similar  triangles 
and  wBR,  we  shall  find 


148  ELEMENTS    OF 

m          TK    X    R  COS  *, 


K  —  r 
where  *  =  75°. 

108.  By  assuming  a  series  of  values  of  pitch  and  number  of 
teeth,  the  value  of  R,  for  each  number  of  teeth,  with  each  given 
pitch,  can  be  found,  and  substituted  in  (2)  and  (3)  where  r  and 
*  are  constant  ;  and  thus  a  series  of  values  of  MT  and  nT  may 
be  obtained  and  tabulated,  expressed  in  twentieths  of  an  inch 
as  on  the  edge  of  the  odontograph,  PL  XXI.,  Fig.  2. 

Such  tables  accompany  the  instrument,  which  may  be  obtained 
from  mathematical  instrument  dealers. 

109.  Teeth  thus  formed  are  analogous  to  those  of  the  first  or 
general  solution,  in  having  both  faces  and  flanks;  but  more 
closely  in  that  any  two  wheels  of  the  same  pitch,  having  teeth 
thus  formed,  will  work  together.     This  appeal's  from  Fig.  46, 
where,  if  AT,  the  pitch  radius  of  one  wheel,  be  changed,  it  will 
only  change  m  and  1ST,  the  centres  of  its  own  tooth  arcs. 

M  and  n,  being  the  centres  for  a  face  and  a  flank  of  B,  all 
the  other  faces  and  flanks  will  have  the  same  radii  MT  +  •£ 
pitch  and  nT  +  %  pitch,  and  their  centres  will  be  in  circles, 
through  M  and  n,  with  B  for  their  centre. 


PROBLEM  IX. 
To  find  Centres  for  approximate  Involute  Teeth. 

By  making  KT  =  &T  infinite,  Fig.  46,  BM  and  B^  will 
coincide  with  BR ;  and  the  two  centres,  thus  united  at  R,  will 
become  that  of  a  single  arc.  A  tooth  profile  of  two  arcs  can 
have  a  point  of  exact  action  for  each  arc  (106),  but  now,  with 
one  arc,  there  can  be  but  one  such  point.  Let  T  be  that  point, 
then,RT  the  tooth  radius  =  R  x  cos  *,  where  R  =  the  radius 
of  the  wheel.  Now  as  the  angle  nTA.  =  *,  is  somewhat  arbi- 
trary, assume  it  at  75°  30',  which  is  otherwise  convenient,  and 
cos  *  =  \  very  nearly,  which  gives 


=  -T-'  a  very  simple  value. 


MACHINE   CONSTRUCTION   AND   DRAWING. 


149 


That  is,  in  approximate  involute  teeth,  let  the  base  circle  be 
tangent  to  a  line,  BC,  Fig.  47,  making  an  angle  of  75°  30'  with 


the  line  of  centres,  AT ;  and  let  the  tooth  radius,  BT,  =  £  AT, 
the  radius  of  the  pitch  circle  DT. 

111.  An  odontograph,  ETF,  for  this  case,  accompanies  the 
larger  one.  Its  angle  ATB  is  made  =  75°  30',  and  its  edge 
TB  is  graduated  in  quarter  inches  ;  so  that  the  radius  of  the 
wheel  being  given  in  whole  inches,  the  same  number  of  quarter 
inches,  read  off  from  T,  when  the  arm  AT  coincides  with  the 
radius  of  the  wheel,  as  in  the  figure,  gives  the  tooth  centre  B. 

Having  divided  the  pitch  circle,  for  the  teeth  and  spaces,  all 
the  other  tooth  curves  will  have  the  same  radius  BT,  and  their 
centres  will  be  in  the  circle  AB. 


EXAMPLE  XXXIY. 

To  construct  Teeth,  having  separate  Faces  and  Flanks,  by 
the  Odontograph. 

Let  the  two  wheels  be  denoted  by  their  centres  A  and  B,  PL 
XXI.,  in  each  illustration.  Let  Fa  denote  face,  and  F£,  flank 
in  the  notation  of  the  figures.  The  general  proportions  of  the 


150  ELEMENTS   OF 

teeth  given  in  the  example  of  the  spur-wheel  are  followed  as 
closely  as  need  be  for  illustration,  remembering  that  5^-1 5ths 
=  a  little  more  than  one-third,  and  6^-15ths,  a  little  more  yet 
(of  the  pitch),  while  a  tooth  occupies  a  trifle  less  than  half  the 
pitch  on  the  pitch  circle. 

The  odontograph  angle,  OTH,  is  not  given  here  of  its  true 
value,  75°,  so  that  the  student  by  only  following  the  text  care- 
fully, and  using  the  figures  of  PL  XXI.  as  guiding  sketches, 
will  be  able  to  construct  the  figures  accurately. 

First :  In  Fig.  1,  let  the  wheel  A  have  a  radius  of  6  ins.  and 
20  teeth.  Then  the  pitch  is  equal  to  the  circumference  divided 

by  the  number  of  teeth  =  ^?=  1.88  ins. 

As  the  pitch  must,  of  course,  be  the  same  for  both  wheels, 
and  as  pitch  and  radius  cannot  be  given,  lest  they  should  afford 
a  fractional  number  of  teeth,  which  it  would  be  impossible  to 
have,  we  must  have  given  the  pitch  and  number  of  teeth,  as  12, 
for  the  other  wheel.  The  product  of  these  gives  the  new  cir- 
cumference, which,  divided  by  2*r,  gives  the  radius, 

P  x  t          1.88  x  12         fl  . 

— — =  3.6  ins. 

2*  3.28 

Now  draw  any  line,  AB,  for  the  line  of  centres,  and  on  it 
place  the  point  T,  the  point  of  contact  of  the  pitch  circles. 
Make  TA,  6  ins.,  scale  •£,  and  A  the  centre  of  wheel  A ;  also 
TB,  3.6  ins.,  and  B  the  centre  of  wheel  B,  and  describe  the  two 
pitch  circles  with  radii  AT  and  BT.  From  T,  lay  off  each  way, 
on  each  pitch  circle,  1.88  inches,  for  the  pitch.  Then  let  a  tooth 
of  A  be  just  below  T ;  and,  accordingly,  lay  off,  downward,  as 
at  Ts,  from  the  upper  end,  as  T,  of  each  pitch,  as  Td,  of  wheel 
A,  a  distance  equal  to  a  little  less  than  half  the  pitch,  say  0.9 
ins.  A  tooth  of  B  will  thus  extend  from  T  upward,  hence  lay 
off  0.9  ins.  upward,  as  at  Tg,  from  the  lower  end,  as  T,  of  each 
pitch,  as  Te,  of  wheel  B.  The  two  sides  of  each  tooth  on  both 
of  the  pitch  circles  will  thus  be  marked.  Next  draw  the  point 
and  root  circles  of  each  wheel  as  usual  (95). 

The  figure  is  now  ready  for  the  application  of  the  odonto- 
graph ;  directly,  if  drawn  in  full  size,  or,  otherwise,  indirectly 
by  laying  off  the  tooth-centres  to  scale.  Consulting  the  table 
of  tooth-centres,  which  accompanies  the  instrument,  and  remem- 
bering that  for  any  given  series  of  wheels  having  the  same  pitch, 


MACHINE   CONSTRUCTION   AND   DRAWING.  151 

it  contemplates  no  wheel  of  less  than  twelve  teeth,  and  that 
then  the  radius  of  the  flanks  is  infinite,  Prob.  VIII.,  we  at  once 
make  the  radial  flanks,  as  gp,  of  B. 

For  the  faces  of  B,  we  have  from  the  table  T— -F#,B,  ^  in., 
which  gives  the  centre,  F#,B  (on  QO),  of  the  first  face,  qr,  on 
the  other  side  of  T.  All  the  other  faces  of  B  have  the  same 
radius,  q— Fa,B,  jusit  used,  and  their  centres  on  the  arc  with  B 
as  a  centre,  and  B— F«,B  as  a  radius. 

For  the  flanks  of  A,  we  have  from  the  table  f-|j-  =  2£  ins., 
which  is  laid  off  from  T  to  the  point  on  OQ,  marked  F^,A,  to 
give  the  centre  of  the  first  flank,  inn,  of  A,  on  the  opposite  side 
of  T.  Then,  as  before  explained  (109),  all  the  flanks  of  A  will 
have  radii  equal  to  F£,A— m,  and  with  centres  on  the  arc 
through  the  first  flank  centre,  F£,A,  and  with  A  for  its 
Centre. 

For  \hefaces  of  A,  we  have  from  the  table  0.6  in.,  to  be  laid 
off  from  T  to  F#,A,  to  give  the  centre  for  the  first  face,  sk, 
below  T  of  wheel  A.  Then,  again,  all  the  other  A  faces  have 
their  centres  on  the  arc  of  radius  A— F«,A,  and  radii  equal  to 
F«,A— s. 

After  this  minutely  detailed  description  of  one  figure,  the 
others  may  be  understood  almost  wholly  by  mere  inspection, 
the  point,  pitch,  and  root  circles,  and  the  divisions  of  the  pitch 
being  laid  out  as  before.. 


' :  In  this  case,  Fig.  3,  the  relative  position  of  the  teeth 
in  contact  at  T  is  the  reverse  of  that  in  Fig.  1 ;  the  tooth  of  the 
H<7^-hand  wheel  being  here  just  above  T.  This  brings  the  75° 
line,  as  it  may  briefly  be  called,  which  represents  the  graduated 
edge  of  the  odontograph,  into  the  position  FZ,A— F£,B.  This 
would  require  the  instrument  to  be  graduated  on  both  sides  oil 
the  edge  MN".  But  this  is  unnecessary,  since  it  can  be  applied 
separately  to  the  two  wheels  in  the  position  similar  to  OQ,  Fig. 
1,  by  applying  it  to  any  radius,  as  BJ,  ending  on  the  upper  side 
of  a  tooth  of  B,  and  to  any  radius,  as  Ac,  ending  on  the  under 
side  of  a  tooth  of  A ;  applying  the  edge  TA,  first  on  Bi,  and 
then  on  Ac. 

But  we  will  proceed  with  the  figure  as  shown,  it  being  drawn, 
as  before,  on  a  scale  of  £. 

In  both  wheels,  the  teeth  and  pitch  are  given,  from  which, 
as  before,  we  find  the  radii,  5.1  ins.,  and  7.64  ins.  The  centre 


152  ELEMENTS    OF 

of  A  is  lost  in  Fig.  1,  the  point  A  on  Fig.  3  merely  indicates  it 
without  showing  its  true  position. 

We  have  then  from  the  table,  for  the  given  pitch  and  num- 
ber of  teeth,  T— FZ,A  =  f$  =  2  ins.,  for  the  centre  of  the  flank, 
ca;  and  T— Fa,  A  =  £$,  for  the  centre,  Fa,  A,  of  the  face,  de,  of 
A.  Likewise,  T-FZ,B  =  ||  for  the  centre,  FZ,B,  of  the  flank, 
fg,  of  B ;  and  T-Fa,B  =  ft  for  the  centre  of  the  face,  Ih,  of 
wheel  B. 

Having  thus  found  four  initial  centres,  one  for  a  face  and  a 
flank  of  each  wheel,  the  remaining  faces  and  flanks  are  drawn 
in  the  same  manner  as  in 'Fig.  1. 

Third  :  Fig.  4  is  varied  from  the  two  preceding  by  using 
a  smaller  pitch ;  and  a  much  larger  radius  for  one  of  the 
wheels.  Also  AB  is  placed  differently. 

Having  the  radius,  r,  and  number  of  teeth,  t,  of  the  upper 
wheel,  we  find  its  pitch  1.6  in.,  which  thus  becomes  that  of  the 
lower  wheel,  which,  having  24  teeth,  has  a  radius  of  6  ins. 

Lay  out  the  pitch,  point  and  root  circles,  and  the  pitch  points 
as  before,  and  draw  OQ  to  make  QTB  =  75°.  Then,  from  the 
table  we  have  for  the  given  pitch  and  numbers  of  teeth,  T — 
FZ,A  =  |f  in.,  for  the  centre,  FZ,A,  of  the  flank  ab,  and  T  — 
Fa,A,  for  =  12£-20ths  for  the  centre,  Fa,A,  of  the  face  cd. 
Likewise,  T— FZ,B  —  f  £  ins.  for  the  centre,  FZ,B,  of  the  flank,  ef, 
of  wheel  B,  and  T— Fa,B  =  4f20ths,  for  the  centre,  F«,B,  of 
the  face,  gh,  of  the  wheel  B.  The  remaining  tooth  curves  can 
be  completed  as  before. 

EXAMPLE  XXXV. 

To  Construct  approximate   Involute  Teeth   ~by  the    Odonto- 
graph. 

This  case,  Fig.  5,  is  drawn  in  full  size,  and  represents  ap- 
proximate involute  teeth,  as  given  by  the  small  odontograph, 
Fig.  47. 

As  in  previous  figures,  the  given  data  are  included  by  a  brace. 
The  line  OQ  is  drawn  so  as  to  make  OTB  (B,  the  centre  of  the 
wheel  PR,  is  in  Fig.  4)  =  75°:30'.  Then,  having  set  out  the 
various  circles  as  before,  with  the  pitch  0.75  in.,  each  way  from 
T,  and  divided  as  before,  read  off  from  T,  on  the  graduated 


MACHINE   CONSTRUCTION   AND   DRAWING.  153 

edge  of  the  instrument,  lying  on  OQ,  the  same  number  of  quarter 
inches,  Prob.  IX.,  that  there  are  of  whole  inches  in  the  radius 
BT,  to  give  #,  the  centre  of  the  curve,  be,  of  a  tooth  having  a 
single  arc  from  point  to  root,  the  part  of  which,  exterior  to  the 
circle  B  —  ank,  represents  the  involute  of  ank  taken  as  a  base 
circle.  In  like  manner,  Td  =  2.6  quarter  inches,  gives  d,  the 
centre  of  the  tooth  are,  ef,  of  the  other  wheel. 

110.  "No  finished  example  is  here   given  of  hyperboloidal 
wheels  (83).     Approximations  to  them  are  known  in  practice 
as  skew-bevels,  and  consist  of  a  pair  of  thin  conic  frusta,  each 
tangent  on  a  circle  of  contact,  to  one  of  the  given  hyperboloids, 
PL  XX.,  Fig.  6.    Teeth  are  then  set  on  these  frusta,  not  in  the  di- 
rection of  their  elements,  but  in  that  of  the  common  generatrix 
of  the  hyperboloids.     Also  the  cones  to  which  these  frusta  be- 
long have  not  a  common  vertex,  since  their  axes  are  the  same 
as  those  of  the  hyperboloids  for  which  they  are  a  substitute. 

111.  PL  XX.,  Fig  9,  is  a  fragment  of  bevel  gears,  of  very  un- 
equal diameters.      Fig.  10   shows   a  form  occasionally   seen, 
where  the  teeth  of  B  are  on  the  interior  of  the  pitch  cone 
generated  by  mV ;  extending  from  its  surface  towards  its  axis, 
and  gearing  with  teeth  on  the  exterior  of  the  wheel  A. 

112.  PL  XX.,  Fig.  8,  shows  a  method  of  communicating  mo- 
tion between  two  given  axes,  AB  and  CD,  which  are  not  in  the 
same  plane,  indirectly,  by  bevel  gear,  instead  of   directly  by 
hyperboloidal  wheels,  as  in  Fig.  6.     In  Fig.  8,  OY  is  an  inter- 
mediate axis,  intersecting  both  of  the  given  ones  ;  then  O  is  the 
common  vertex  of  the  bevel  wheels,  m  and  n ;  and  Y  is  the 
common  vertex  of  the  bevel  wheels,^?  and  q.     As  the  figure  is 
drawn,  AB  and  OY  are  in  the  plane  of  the  paper,  and  CD  is 
out  of  it. 

The  parts,  n  and  p,  of  the  intermediate  double  frustum  need 
not  be  in  one  piece  as  shown,  but  may  be  separate,  and  any- 
where on  OY,  to  suit  the  positions  of  m  and  q  on  their  axes. 


EXAMPLE  XXXYI. 
Projections  of  Bevel  Gearing. 
PL  XXII.  shows  a  very  beautiful  example  of  bevel  gear. 


154:  ELEMENTS   OF 

By  lettering  like  points  with  the  same  letters,  capital  or  small, 
on  this  and  on  PI.  XX.,  but  little  is  left  to  be  explained. 

As  the  flanks  are  radial,  the  generating  or  describing  circles 
in  the  development  are  drawn  with  radii,  AT  and  BT,  equal  to 
half  of  the  elements,  V"b,  and  v"b  =  v'"T,  of  the  cones  contain- 
ing the  outer  ends  of  the  teeth  and  having  the  pitch  circles,  m~b 
and  MS,  for  their  bases. 

The  pitch  cones  (100)  of  the  two  wheels  have  a  common  ver- 
tex Y — V",  and  element  of  contact  V& — ~N'"in" . 

Designating  the  wheels  by  their  pitch  circles,  or  centres,  the 
wheel  ml) — m"a"  is  drawn  by  first  making  its  circular  projection 
O'.  Likewise,  M&  is  made  from  the  circular  projection,  V" — 
M'dT,  of  the  same  wheel. 

The  student  may  assume  a  scale,  and  from  that  determine 
the  measurements. 

Wheels  of  given  radii  act  together  better,  the  more  teeth 
they  have  ;  hence,  as  the  arc  of  action  of  bevel  teeth,  at  their 
outer  extremities,  for  example,  is  in  the  plane  V'fo/'  (perpen- 
dicular to  the  paper)  and  virtually  with  radii  V"5  and  v"b,  the 
action  of  the  bevel  wheels,  with  nominal  radii  ab  and  db,  is 
equivalent  to  that  of  spur  wheels  with  radii  V'b  and  v"b. 


c— Warped   Communicators. 
EXAMPLE  XXXVII. 

The  complete  Projections  of  a  Screw  and  Nut. 

Description. — If  a  square,  Aa — A'a'r's',  PL  XXIII.,  Fig.  1, 
revolve  uniformly  around  an  axis,  O — O'O",  and  at  the  same 
time  move  parallel  to  the  axis,  and  uniformly,  it  will  describe 
the  winding  or  spiral  rail,  thread,  or  solid  ADG  gda — A'a'r's, 
G'G"  g"g ',  M'M"  m!'m' .  This  surface  is  bounded  as  follows : 
Its  outer  surface,  generated  by  A — AY,  during  the  movement 
of  the  square,  is  cylindrical  and  vertical  in  this  case.  Its 
inner  surface,  generated  by  a — a'r',  is.  also  cylindrical  and 
vertical.  Its  upper  and  lower  surfaces  generated  by  Aa — s'rf, 
and  Aa — A'a',  respectively,  are  called  right  helicoids  :  called 
helicoids  from  the  form  of  the  bounding  curves,  as  ADG — 
A'D'G',  which  is  a  helix  /  and  called  right  helicoids,  because 
Aa — A'a'  and  Aa — r's'  are  perpendicular  to  the  axis  O — O'O". 


MACHINE   CONSTRUCTION   AND   DRAWING.  155 

Now  let  equidistant  threads,  like  that  just  described,  be 
formed,  solid  with  an  interior  cylinder  or  core,  adg — a'TTJ'V, 
and  the  result  will  be  a  square  threaded  screw.  The  height, 
AM',  to  which  the  point  A  ascends,  in  one  revolution  around 
the  axis,  O — O'O",  is  the  pitch  of  the  screw.  As  the  spaces, 
as  t'G,  between  the  threads  must  be  equal  to  the  threads,  in 
order  to  receive  the  corresponding  threads  of  the  internal 
screw,  Fig.  2,  it  follows  that  A'M'  must  be  some  even  number 
of  times  AY,  the  height  of  a  thread.  Here  A'M'^6  AY,  and 
the  figure  represents  a  three-threaded  screw,  the  threads  W 
and  X'  being  separate  and  distinct,  intermediate  between  the 
thread,  A'aY  G-',  which  reappears  at  M'M"  m"  O". 

Fig.  2,  as  indicated  in  the  plan,  shows  the  interior  of  the 
back  half  of  the  internal,  or  hollow  or  concave  screw,  within 
which  the  solid  screw  works.  It,  of  course,  has  the  same  pitch 
as  the  screw. 

From  this  description,  and  remembering  that  both  motions  of 
the  generating  points  and  lines  of  the  threads  are  uniform,  we 
have  the  following  construction : — 

Construction. — For  the  screw,  begin  with  the  concentric 
semicircles,  OA  and  Oa,  of  the  plan,  using  a  scale  of  not  less 
than  one-half,  and  divide  these  semicircles  into  six  equal  parts, 
as  shown,  to  indicate  the  uniform  angular  motion  of  Aa — A! a'. 
Lay  off  XX  =  3"  from  the  ground  line,  A7N',  on  a  vertical 
line,  and  divide  it  into  twelve  equal  parts  indicating  the  uniform 
ascent  of  AA',  etc.,  during  a  whole  revolution.  Then  A.  being 
projected  at  A',  on  the  ground  line,  and  on  every  second  line, 
as  s'c',  above  it ;  B  will  be  projected  on  the  first,  third,  fifth, 
etc.,  line  from  the  ground  line ;  C  on  the  ground  line  and 
every  second  line  above ;  D,  like  B,  and  so  on. 

At  first  it  may  be  better  to  construct  onty  one  thread  in 
elevation  as  indicated  by  A'B'C',  etc.,  which  will  guide  the  eye 
in  constructing  the  other  threads.  In  any  case  it  will  be  better 
to  complete  the  outer  helices  before  beginning  the  inner  ones, 
since  only  certain  portions  of  the  latter  are  visible.  Also,  after 
completing  the  outer  helices,  the  threads  are  to  be  distinguished 
from  the  spaces,  by  marking  the  former  in  pencil  in  some  way 
on  both  sides,  as  by  the  letters  W  and  X'. 

The  elements  Aa — A' a' ;  BJ — B'&',  etc.,  of  the  helicoidal 
surfaces  being  horizontal,  project  up  a  at  a'  /  J,  at  V  on  the 
first  line,  B'J'  /  c,  at  c',  etc.,  and  for  one  thread,  construct,  com- 


156  ELEMENTS   OF 

pletely,  all  the  four  helices  of  that  thread,  beginning  as  at 
A'a'r'  and  s' ;  which  will  show  clearly  the  number  of  distinct 
threads  in  the  screw. 

For  the  remaining  threads,  construct  only  the  visible  portions 
of  the  inner  helices,  viz. :  the  upper  portion,  as  d"g" ,  on  the 
right-hand,  half  of  each  thread ;  and  on  the  lower  side,  as  at 
a'd',  on  the  left-hand,  half. 

Small  portions,  as  t'Y  and  M'L',  of  the  ~back  half  of  the 
outer  helices,  or  the  same  portions  of  the  threads  as  just  named, 
will  be  visible.  And  portions  of  the  extreme  elements,  as  from 
u'  upwards,  and  from  mf  downwards,  of  the  cylinder  of  the 
screw  are  seen. 

The  curves  of  the  elevation  are  to  be  mostly  drawn  with  an 
irregular  curve,  using  the  same  portion  reversed  for  D'G'  that 
was  used  for  drawing  AT)',  making  the  two  parts  unite  smoothly 
at  D' ;  and  observing  that  A'D',  a'd',  and  all  like  parts  are  con- 
vex upward,  while  their  counterparts,  D'G'  and  d'g',  are  con- 
vex downward.  Also,  as  the  helix  is  a  continuous  curve,  and 
not  pointed,  it  is  of  prime  importance  to  have  the  helices  truly 
tangent,  as  at  G',  G",u',  s',  m',  etc.,  to  the  vertical  elements,  as 
G'G"  and  a'r'. 

The  plan  is  inked  in  strict  agreement  with  the  elevation, 
showing  a  horizontal  section  of  a  thread  at  CceE. 

To  vary  the  exercise,  the  student  should  make  a  one,  or  a  two- 
threaded  screw,  or  divide  ADG  into  eight  instead  of  six  equal 
parts,  or  cut  off  the  screw  by  a  different  horizontal  plane,  as 
M"m",  or  LT. 

The  Nut,  or  Internal  Screw,  Fig.  2. — This  construction  re- 
quires little  further  explanation.  Having  the  same  dimensions 
of  threads  as  the  screw,  and  the  same  pitch,  the  projections  of 
its  visible  helices  in  the  inside  of  the  hinder  half  are  found  as 
before,  and  must  be  inclined  in  the  same  manner  as  threads 
G'M"  on  the  back  of  the  screw.  Here  the  inner  helices  are 
visible  all  across  the  elevation,  while  the  outer  ones,  as  G'J'M', 
are  only  visible  on  the  under  left-hand  sides  of  the  threads,  and 
on  their  upper  right-hand,  sides,  as  at  G"l". 

Note  that  a  space,  as  A."r",  of  the  nut  corresponds  with  a 
thread,  as  A'r',  Fig.  1,  of  the  screw,  while  a  thread,  as  K'S',  of 
the  nut  is  between  the  same  horizontal  lines  as  the  space  G't' 
of  the  screw.  The  figure  otherwise  explains  itself. 


MACHINE   CONSTRUCTION    AND   DRAWING.  157 

EXAMPLE  XXXYIIL 
The  Abridged  Drawing  of  Screws. 

When  either  the  scale  or  the  pitch,  employed  in  representing 
a  screw,  is  so  small  as  to  make  the  apparent  curvature  at  points 
00'  6, 6',  etc.,  PI.  III.,  Fig.  9,  so  sharp  as  to  be  sensibly  pointed, 
the  helices  may  be  thus  pointed  in  vertical  projection,  or,  in 
general  terms,  in  the  projection  on  a  plane  parallel  to  the  axis 
of  the  screw. 

The  figure  illustrates  this  modification  in  the  drawing  of  a 
<m0-threaded  screw  of  a  screw,  of  8  inches  outside  diameter,  on 
a  scale  of  one-fourth. 

Similar  points  in  the  two  projections  are  numbered  with  the 
same  figure,  a  very  convenient  method  in  many  cases. 

PI.  III.,  Fig.  10,  represents  a  triangular  threaded  screw  of 
two  threads,  to  the  same  scale  and  dimensions,  except  pitch,  as 
the  last  one.  Here  the  thread  is  generated  by  the  isosceles 
triangle,  a'Q'Q",  whose  base,  ao6",  is  vertical.  In  this  case,  the 
space  between  two  threads  extends  from  the  middle  of  one 
thread  to  the  middle  of  the  next,  as  from  0'  to  b' '.  Hence, 
although  the  screw  is  plainly  two-threaded,  as  seen  by  following 
an  outer  helix,  0',6',12'j  yet  the  pitch,  O',12',  is  but  twice  the 
height,  a'§" ,  of  a  thread ;  while  in  the  square-threaded  screw, 
Fig.  9,  a  pitch,  Q'b',  of  double  the  height,  a'b' ' ,  of  a  thread  gives 
only  a  ow<?-threaded  screw.  To  have  made  Fig.  10  one-threaded, 
we  should  have  made  O'J'  the  pitch,  and  made  the  horizontal 
lines  half  as  far  apart  as  now,  and  projected  6  upon  the  hori- 
zontal line  through  a'.  The  helix  beginning  at  0'  would  then 
have  reappeared  at  V. 

The  student  should  construct  a  triangular-threaded  screw  on 
a  large  scale,  as  partly  shown  on  PI.  XXIII.,  Fig.  3 ;  also  the 
internal  screw  for  the  same.  Strictly,  the  visible  contour  of  a 
helicoid  is  curved,  being  tangent  to  the  successive  elements,  but 
is  nearly  straight  for  so  short  a  distance  as  ab  /  hence  it  is  a  suf- 
ficient refinement  of  construction,  unless  the  scale  is  very  large, 
to  make  ab  straight,  but  tangent,  as  at  a  and  b,  to  the  outer  and 
inner  helices,  instead  of  running  from  A  to  n,  as  in  PL  III., 
Fig.  10. 

All  the  helices  shown,  but  by  straight  lines. — PI.  III.,  Figs.  11 
and  12,  illustrate  this  abridgment.  The  curvature  of  a  helix, 


158  ELEMENTS   OF 

as  seen  in  these  figures,  is  so  slight  that  the  idea  of  a  screw 
is  well  suggested  by  making  the  helices  straight.  In  Fig.  11 
AC  is  the  pitch,  and  the  screw  is  two-threaded.  Points,  as  c 
and  <P,  are  in  the  same  horizontal  line,  as  in  PI.  XXIII.,  Fig.  1 ; 
and  generally  all  parts  arc  shown  just  as  in  that  figure,  except 
that  they  are  made  straight,  and  therefore  only  their  extreme 
and  middle  points,  as  A,B ;  e  and  •/•,  and  ;i,  need  to  be  noted  be- 
fore drawing  them.  This  is  sufficiently  done  by  drawing  hori- 
zontal lines  at  a  distance  apart,  B£,  equal  to  the  thickness  of  a 
thread,  together  with  the  five  vertical  lines  through  Ac,  e,  dn, 
ar,  and  B  ;  where  ce  =  dB  =  B#,  and  Be?  =  df. 

In  like  manner,  Fig.  12  is  like  Fig.  10.  AC  is  the  pitch  = 
2A/"/  Ac  =  de  and  AD  =  De,  and  the  horizontal  lines  need  only 
be  drawn  at  a  distance  apart  equal  to  ca. 

The  student  should  repeat  these  constructions  for  a  one  or  a 
Mree-threaded  screw. 

AC,  Fig.  13,  =  4Cc  for  a  two-threaded,  2Cc  for  a  0ra-threaded 
screw,  6Cc  for  a  three-threaded  one,  etc. 

AC,  Fig.  12,  =  2A/=  4ac  for  a  two-threaded  screw;  A/,  for 
a  era-threaded  screw,  etc. 

Outer  Helices  only  shown. — Fig.  14  shows  a  further  abridg- 
ment, where  so  much  of  the  outer  helices,  only,  as  are  on  the 
front  half  of  the  screw  are  shown. 

Smaller  Triangular  Screws. — Fig.  15  illustrates  a  screw  with 
triangular  threads,  in  which  the  greater  steepness  of  the  inner 
helix  is  neglected,  and  the  outer  and  inner  helices  are  made 
parallel,  the  former  being  inked  heavy. 

Very  Small  Screws. — These  are  represented  in  Figs.  15-17. 
Sometimes  only  the  helices  are  drawn,  omitting  the  end  lines  of 
the  threads.  The  effect  is  better  on  the  triangular  thread,  Fig. 
16,  than  on  the  square  thread. 

Finally,  Fig.  15  represents  the  helices  as  all  equal,  parallel, 
and  straight,  and  included  between  two  parallel  lines. 

Fig.  17  is  a  screw  bolt,  that  is,  a  bolt  or  short  rod  threaded  to 
receive  a  nut  at  one  end,  and  headed  at  the  other. 

Uniform  System  of  Sweats. 

112.  The  extent  to  which  screws  enter  into  the  composition  of 
machines,  either  as  fastenings  or  communicators  of  motion,  and 
the  distances  from  the  place  of  manufacture  to  which  machines 


MACHINE   CONSTKUCTION   AND   DKAWESTG.  159 

are  often  transported,  and  at  which  they  must  be  repaired,  make 
it  very  desirable  that,  at  least  for  screws  used  for  fastenings, 
there  should  be  a  uniform  system  of  threads  and  nuts. 

Screws  used  for  communicating  motion  may  be  subject  to  so 
many  special  conditions  as  to  make  the  use  of  an  invariable 
series  of  them  impossible. 

Such  system  as  that  just  mentioned  is  used  in  England,  and 
it  is  of  constantly  increasing  importance  that  the  like  should  be 
employed  in  this  country.  The  following  carefully  matured 
system,  proposed  in  1864  by  William  Sellers  of  Philadelphia,* 
is  therefore  given  as  a  contribution  to  this  desirable  result.  It 
consists  of  the  following  notation,  formulas,  and  a  table  of  sizes, 
from  which  a  few  examples  are  here  taken.  They  relate  only 
to  triangular-threaded  screws. 

D  =  external  diameter  of  screw. 

a  =  constant  subtrahend,  2.909. 

b  —  constant  divisor,  16.64. 

c  =  D  expressed  in  16ths  of  an  inch,  plus  10. 

d  —  internal  diameter,  or  that  at  the  bottom  of  the  threads.        =: 
p  =  the  pitch,  meaning,  in  this  table,  the  distance  between  the 

threads.  = 

n  =  number  of  threads  per  inch,  the  nearest  whole  number  to       — 

P 
w  =  width  of  the  flat  top  and  bottom,  that  is,  of  the  outer  and 

inner  edges  of  threads.  =  f 

o 

I  =  least  diameter  of  finished  nuts  and  bolt-heads  =  perpendicu- 
lar between  opposite  sides,  or  diameter  of  inscribed  circle,  f  D  + 

7t  =  long  diameter  of  hexagonal  nuts,  or  bolt-head  =  diameter 

of  circumscribing  circle.  =  I  x  1.155 

8  =  Do.  of  square  nuts  or  bolt-heads.  =  I  x  1.414 

t  =  thickness  of  finished  nut  or  bolt-head.  =  D  —  -^  in. 

The  threads  are  to  be  truncated  as  at 
Fig.  48,  to  give  increased  strength  both  to 
the  thread  and  the  bolt,  and  the  angle 
abc  is  fixed  at  60°,  that  being  much  easier 
to  verify  than  the  English  one  of  55°, 
besides  giving  a  more  substantial  thread. 
The  following  table  presents  a  few  examples,  and  the  dimen- 
sions of  only  finished  nuts  and  bolt-heads.     All  the  dimensions 
are  in  inches  and  fractions  of  an  inch. 

*  Essay  on  a  System  of  Screw-Threads  and  Nuts. 


160 


PROPORTIONS   OF   SCREWS,   THREADS,   NUTS,   AND  BOLT-HEADS. 


D. 

n 

d 

w 

I 

tf 

A 

8 

i 

20 

.185 

.0062 

A 

A 

.505 

.618 

+ 

13 

.400 

.0096 

I* 

5 

.938 

1.161 

11 
9 

.507 
.731 

.0113 
.0138 

j   i 
i    i* 

A 

11 

1.155 

1.588 

1.414 
1.944 

1 

8 

.837 

.0156 

ift 

It 

1.805 

2.209 

lf 

7 

1.065 

.0178 

!  m 

!VV 

2.238 

2.740 

H 

6 

1.284 

.0208 

i    2A 

2.671 

3.270 

2 

4i 

1.712 

.0277 

8S 

lj| 

3.537 

4.330 

2* 

4 

2.176 

.0312 

8tf 

** 

4.403 

5.391 

EXAMPLE  XXXIX. 
Endless  Screws  and  Spiral  Gear. 

Description. — An  axis  revolving  in  fixed  supports,  and  hav- 
ing a  screw  thread  cut  upon  its  circumference,  is  an  endless 
screw.  Because  such  a  screw  makes  no  advance  in  the  direc- 
tion of  its  axis,  it  will  advance  or  move  any  yielding  piece  on 
which  its  thread  can  act.  One  complete  revolution  of  the  screw 
will  advance  the  point  upon  which  it  acts  a  distance  equal  to 
the  pitch  of  the  screw.  If,  then,  the  thread  engages  with  a 
wheel  whose  teeth  are  so  set  as  to  be  tangent  to  the  thread, 
when  in  contact  with  it,  the  screw  will  give  a  slow  rotation  to 
the  wheel. 

PL  XXXI.,  Figs.  1  and  2,  shows  such  an  arrangement. 
OO'K— O"K'  is  a  wheel  actuated  by  the  screw  HAB— B'L. 

In  this  case  the  screw  thread  is  formed  in  the  usual  manner ; 
therefore,  by  taking  a  section,  c'HB,  through  the  centre  of  the 
body  of  the  wheel  and  the  axis  of  the  screw,  we  shall  have  the 
equivalent  plane  rack  driving  a  spur  wheel.  This  problem  is 
here  solved  by  the  system  of  involute  teeth  (IVth  Sol.),  but 
with  the  pitch  line,  LI/,  or  exterior  element  of  the  outer  cylin- 
drical surface  of  the  screw  as  the  generating  line.  The  invo- 
lutes of  LI/,  generated  by  the  unwinding  of  LI/  from  itself, 
will  be  straight  and  perpendicular  to  LL/  as  at  ac,  Fig.  4,  and 
the  corresponding  involute  teeth  of  the  wheel  will  be  involutes 
of  its  base  circle,  O — O'K,  tangent  to  LL',  as  at  a5.  Fig.  4. 


MACHINE   CONSTRUCTION   AND    DRAWING.  161 

Construction. — The  screw  being  constructed  as  usual,  and  as 
shown,  the  inclined  teeth  of  the  wheel  are  thus  drawn.  First 
lay  out  the  circular  elevation,  O — O'K,  of  the  front  of  the 
wheel  as  just  described,  with  involute  teeth.  Then  develop 
any  convenient  arc,  as  AB — A'B',  of  an  outer  helix  of  the 
screw,  into  the  tangent  plane  AD — AVD',  at  AD — A'D',  by 
making  AD  =  AB,  and  projecting  D  at  D',  on  a'~D'  drawn 
through  B',  and  perpendicular  to  the  axis  a'Af.  Then  D'A'  is  a 
tangent  to  the  helix  at  A' ;  and,  by  the  properties  of  tangents 
to  a  helix,  has  the  same  inclination  to  a  plane  perpendicular  to 
the  axis,  A'H',  that  the  helix  has ;  moreover,  this  inclination  is 
constant. 

The  teeth  of  the  wheel  will  now  be  inclined  to  the  straight 
elements  of  its  cylindrical  rim  by  the  angle  a'D'A',  the  com- 
plement of  the  inclination  a'A'D,  of  the  thread  to  the  screw 
axis  A'H'. 

"We  now  turn  aside  to  rehearse,  for  convenience,  the  construc- 
tion of  a  helix,  A'B',  Fig.  3,  from  its  plan,  AB,  and  develop- 
ment, A"B",  which  is  straight,  and  found  by  unrolling  into  a 
plane  any  convenient  portion  of  the  vertical  cylinder  ABC — 
A'C'B',  on  which  the  helix  lies ;  so  that  here  A"C"  =  A3C. 
Then  any  point,  as  1,  of  A'B',  is  the  intersection  of  the  projec- 
ting line  1 — 1  perpendicular  to  A'C',  with  the  line  1 — 1  paral- 
lel to  A'C". 

Returning  now  to  Fig.  1,  and  proceeding  likewise,  make 
dD'a'  =  90°  and  A'D'C  =  90°,  to  make  CD'd  =  a'D'A',  and 
we  shall  have  the  inclination  of  the  teeth  of  the  wheel  relative 
to  the  projection,  O'O",  of  its  axis,  but  on  the  under  side  of 
the  wheel. 

Draw  E'V,  Fig.  2,  so  as  to  have  E' W"  =  CDW  =  A'D  Vy 
and  E'V  will  then  be  the  development  of  a  portion  of  one  heli- 
cal edge  of  a  tooth  of  the  wheel,  analogous  to  A"B"  in  Fig.  3. 
For  convenience,  take  the  lines  ~L'n',  He',  and  K'J'  produced, 
and  others  at  the  same  distance  apart,  as  E'E"  and  e'e",  to  cor- 
respond to  a'a",  b'b" ',  etc.,  Fig.  3.  Then,  by  drawing  E'V' 
perpendicular  to  them,  and  dividing  e"e'"  into  four  equal  parts, 
as  E'V  is,  we  have  e"e'"  corresponding  to  AD  =  AB  =  03. 
(at  the  left  of  the  screw)  for  the  screw.  Hence  lay  off  e"e"' ', 
and  its  divisions  at  F/^  on  the  tangent  FG,  and  so  that  one  of 
the  divisions  shall  fall  at  c,  the  point  of  a  tooth.  Transfer  these 
points  to  the  circle  of  radius  OF,  as  at  FE,  and  we  shaE 
11 


162  ELEMENTS    OF 

the  horizontal  projection,  we  will  call  it  for  the  moment,  corre- 
sponding to  A3B,  Fig.  3,  of  the  helical  portion  whose  develop- 
ment is  ~E"e". 

The  vertical  projection,  <?'E',  is  now  found  just  as  A'B'  was  in 
Fig.  3,  as  is  seen  by  the  lines  of  construction,  and  the  use  of 
the  same  letter/  for  the  same  point.  Owing  to  the  very  great 
pitch  of  the  wheel,  considered  as  a  screw,  which  it  now  plainly 
is,  e'n'c'V^  is  sensibly  straight,  and  FE  is  sensibly  the  same  as 
J?f.  Thus  we  have  verified,  by  a  full  construction,  the  pro- 
priety of  making  all  the  longitudinal  lines  of  the  tooth  of  a 
•worm  wheel,  or  spiral  gear,  parallel  straight  lines. 

Projecting  V  back  to  b,  we  find  cb  for  the  projection  of  the 
length  of  the  tooth  on  the  projection  OO'K.  Hence,  to  com- 
plete that  projection,  make  pq  =  cb,  and  do  the  same  for  all 
the  teeth,  and  make  the  back  curves,  as  from  q,  the  same  as  the 
front  ones,  as  from^>. 

Observe  that,  as  successive  teeth  of  the  wheel  come  in  con- 
tact with  the  same  thread,  B'L,  of  the  screw,  and  in  the  same 
relative  position,  they  are  not  successive  portions  of  the  same 
thread,  but  like  portions  of  different  threads  ;  that  is,  the  wheel, 
considered  as  a  screw,  has  as  many  threads  as  it  has  teeth. 
Hence  the  other  teeth  on  the  projection,  O"K'L',  are  found  by 
projecting  from  the  other  figure,  O — O'K,  where  the  teeth  all 
appear  alike. 

Often  the  section  of  the  screw  thread  is  of  the  same  form  as 
a  wheel  tooth,  that  is,  with  a  separate  face  and  flank.  In  that 
case  the  wheel  teeth  would  be  likewise  formed  by  an  appro- 
priate generating  circle,  according  to  the  first  or  second  solution. 

Further,  to  give  the  screw  tooth  a  larger  surface  of  contact 
with  the  wheel  teeth,  the  point  and  root  lines  of  the  wheel 
teeth,  in  other  words,  all  parts  of  the  face,  n'b'KL',  of  the 
wheel,  are  concave  arcs  of  the  radii,  IIB  and  Hm,  of  the  screw 
thread.  In  such  a  case  points  would  be  constructed  on  the  two 
plane  sides,  K'&'  and  L'n',  and  in  the  central  section,  He',  of 
the  wheel. 

With  this  description  of  all  that  is  peculiar  to  the  case,  the 
student  can  readily  construct,  on  a  large  scale,  a  few  such  teeth. 


MACHINE   CONSTRUCTION    AND   DRAWING.  163 

EXAMPLE  XL. 

Detailed  Construction  of  a  Tooth  in  Spiral  Gearing. 

Description. — The  term  spiral  gear  is  applied  to  a  species  of  spur 
wheel  in  which  the  teeth  are  formed  as  in  the  wheel  OO'K — 
O"L'K',  PL  XXXI.  A  pair  of  such  wheels,  vritii  parallel  axes, 
act  together  with  a  peculiar  smoothness  and  stillness,  because  a 
pair  of  teeth  begin  contact  at  one  end,  and  their  point  of  con- 
tact shifts  continuously  to  their  other  end,  with  a  rolling  motion 
between  the  teeth,  and  just  as  one  pair  are  about  to  quit  each 
other  another  pair  will  begin  contact. 

PL  XXXI.,  Fig.  5,  shows  an  approximate  form  of  this  gear- 
ing, in  which  a  wheel  is  formed  of  a  series  of  thin  plates,  each 
of  which  is  a  spur  wrheel,  but  set  a  little  in  advance,  angularly, 
of  the  next  one,  as  indicated  by  the  black  spaces,  which  repre- 
sent teeth. 

Construction. — PL  XXI.,  Fig.  6.  Let  O  be  the  centre  of  the 
wheel,  and  Om,  Og,  and  Ob,  the  radii  of  the  point,  pitch,  and 
root  circles,  Og  being  4f  ins.  Lay  out  by  curves  with  any 
suitably  assumed  radii,  taken  merely  for  illustration,  the  cross 
section  of  a  tooth  in  plan,  at  cibcdef  (at  the  left),  and  let 
there  be  20  teeth,  and  1£  inches  pitch.  Make  the  two  radii? 
Oa,  and  Oa,  45°  apart,  so  that  aa  shall  be  one-eighth  of 
the  circumference  of  the  pitch  circle.  Then  let  O'O", 
=  8  inches,  be  the  ascent  of  the  tooth  section  during  one- 
eighth  of  a  revolution.  That  is,  the  pitch  of  the  teeth 
threads  is  64  inches.  Then  we  have  only  to  construct  in  the 
usual  way,  Ex.  XXXVII.,  as  shown  by  the  projecting  lines 
and  letters  of  reference,  the  six  portions  of  helices,  beginning 
at  the  points  a,  b,  c,  d,  e,  and/"  (on  the  left).  The  equal  pitch 
for  the  different  radii,  Ob,  Oa,  and  Oc  is  regarded  by  dividing 
bb  and  O'O"  into  the  same  number  of  equal  parts,  four  in  this 
case.  Divide  aa,  and  O'O",  each  into  four  equal  parts,  and  ce 
and  OO"  in  like  manner,  also  ff,  ee,  and  dd.  Now  bf,  the 
width  of  the  tooth  at  the  root,  happens  to  be  the  fourth  part  of 
bb.  Then,  by  the  radii  Ob  and  Of  produced,  we  find  g7i  == 
one-fourth  of  aa  to  be  laid  off  from  a  and  e  four  times  to  the 
right ;  and  mn  =  one-fourth  of  cc,  to  be  laid  off  four  times  on 
mn"  from  c  and  d  (on  the  tooth)  1. 

Having  constructed  the  helical  arcs,  by  projecting  up  the 


164  ELEMENTS    OF 

points  thus  found,  assume  PQ  as  a  segment  of  the  face  of  the 
wheel  and  all  those  portions  of  these  helices  within  its  limits 
will  be  real  lines  of  a  tooth. 

As  to  visibility,  the  left  root  curve  is  visible  from  V"  down 
toj?,  where  it  runs  out  of  sight;  the  left  pitch  helix  is  visible 
from  a"  down  to  r  ;  the  two  point  helices  are  visible  through- 
out, and  so  is  the  right-hand  pitch  helix,  e'e" ,  while  the  right- 
hand  root  helix  is  visible  from/"  up  to  t. 

113.  In  regard  to  the  manufacture  of  worm  wheels,  of  con- 
cave face,  to  act  with  endless  screws,  the  difficulty  of  represent- 
ing the  teeth  whose  parallel  sections  are  dissimilar,  owing  to  their 
different  position  relative  to  the  successive  meridian  sections  * 
of  the  screw,  is  obviated  by  making  a  model  screw  of  hardened 
steel,  and  notched  on  the  edges  of  its  threads.  It  is  thus  made 
into  a  cutter,  and  will  itself  cut  the  proper  teeth  on  the  concave 
face  of  the  wheel,  when  both  are  revolved  together  with  the 
proper  relative  velocity. 

By  a  similar  expedient,  and  by  attaching  a  cutter  to  the 
wheel,  it  is  possible  to  form  an  endless  screw  like  that  shown  in 
PI.  XXI.,  Fig.  8,  where  the  threads  are  in  contact  with  a  large 
number  at  once  of  the  wheel  teeth,  and  in  the  central  plane 
ABC  of  the  two  bodies. 

*  A  section  made  by  a  plane  containing  the  axis. 


MACHINE   CONSTRUCTION   AND   DRAWING.  165 


CLASS  IY.-BEGULATORS. 

114.  Under  the  head  of  regulators,  steam  governors  might 
naturally  occur  to  the  mind  at  once ;  but  it  must  be  considered 
that  governors  are  not  single  mechanical  elements  in  the  sense 
of  those  hitherto  represented  ;  rather  they  are  secondary  ma- 
chines, attached  to  their  principals,  which  they  govern.  That 
they  truly  are  machines  is  evident  from  the  definition  (28), 
since  they  always  consist  of  a  train  of  connected  pieces,  em- 
bracing some  or  all  of  the  following,  viz.,  band  wheels,  spur  or 
bevel  wheels,  pistons,  racks,  connecting  rods,  screws,  oscillating 
arms,  etc. ;  receiving  motion  as  a  whole  at  some  point,  and 
communicating  it  through  the  train  of  pieces  to  another  point. 

Hence,  as  there  would  be  little  interest  or  use  in  separately 
describing  or  drawing  the  essential  governing  member  alone, 
whether  ball,  or  fan,  etc.,  the  further  description  of  governors 
is  postponed  till  the  chapters  on  compound  elements  of  ma- 
chines. 

A— Point  Regulators. 

Governor  balls  belong  under  this  head. 


B — Line  Regulators. 

EXAMPLE  XLI. 
A  Fly   Wheel. 

Description, — A  fly-wheel  is  here  reckoned  as  reduced  to  its 
rim,  and  that  a  heavy  line.  It  is  an  equalizer  of  velocity  by 
being  an  equalizer  of  work,  which  is  its  principal  function. 
That  is,  when  the  load  is  largely  or  wholly  taken  off,  the  inertia 
developed  in  the  fly  wheel,  by  the  gradual  increase  of  velocity 
which  follows,  results  in  a  storing  up  of  work  which  is  usefully 


166  ELEMENTS    OF 

given  out  in  the  maintenance  of  a  slowly  retarded  velocity, 
when  a  return  of  the  full  load  takes  place. 

The  greater  the  difference  between  the  extreme  loads  carried 
by  the  engine,  compared  with  the  power  of  the  latter,  and  the 
less  the  time  in  which  the  extreme  load  is  brought  on,  the  heav- 
ier should  be  the  fly  wheel. 

Accordingly,  the  heaviest  fly  wheels  are  found  in  rolling- 
mills  for  example,  where  the  rolls,  Ex.  XVII.,  are  alternately 
empty,  and  run  with  very  little  power ;  and  then  full,  and  ope- 
rating against  a  prodigious  resistance,  especially  in  case  of  steel 
rolling  mills,  where  rolls  nearly  a  foot  thick  are  sometimes 
snapped  in  two. 

PI.  XXIV.,  Fig.  1,  represents  a  sketch  on  various  scales ;  or 
no  scale,  in  some  parts,  of  a  sixty-ton  fly-wheel  at  the  Bessemer 
Steel  "Works  at  Troy,  K  Y. 

It  is  made  in  ten  segments,  as  AB  and  the  arm  E,  weighing 
five  tons  each.  The  massive  hub,  and  ten  3-J-  inch  rods,  as  F', 
make  the  total  weight  sixty  tons  or  more  ;  whereas  twenty -five 
tons  is  the  weight  of  quite  a  heavy  wheel. 

The  section  of  the  rim  is  19  ins.  by  20  ins.,  and  each  segment 
is  filed  smooth  at  the  ends  of  the  rim  portion,  AB,  on  all  the 
parts  which  are  shaded  in  the  end  view,^/^'.  Adjacent  seg- 
ments are  then  strongly  bound  together,  as  at  pq — -p'p" •>  by  stout 
links,  D,D",  made  of  wrought  iron,  2|-  ins.  square.  The  inner 
ends  of  the  arms  are  then  turned,  15|-  ins.  long,  and  8  ins.  di- 
ameter, and  keyed  to  the  hub,  as  shown  at  s,  and  o.  The  ra- 
dius rods,  F',  are  likewise  keyed  into  the  hub,  and  headed  as  at 
u,  to  set  into  the  head  socket  u'. 

There  being  ten  segments,  no  arm  will  be  horizontal  if  one 
be  vertical  as  at  E  ;  yet  to  show  both  a  face  view,  ^KL,  and  an 
edge  view,  et,  of  an  arm,  and/",  of  a  radius  rod,  the  two  latter 
are  shown  in  a  horizontal  position,  in  plan.  tnWt,"  is  the  hol- 
low interior  of  the  hub,  bored  on  the  two  sides  as  at  ab — a'V  to 
receive  the  main  shaft,  to  which  it  is  heavily  keyed. 

Construction. — Three  segments,  or  at  least  two,  should  be 
constructed  in  full  in  both  projections,  and  on  a  scale  of  not  less 
than  half  an  inch  to  one  foot.  The  section  p'q'  of  the  rim 
may  well  be  made  on  a  scale  of  one  inch  to  one  foot ;  and  the 
plan  should  be  complete,  from  the  horizontal  bearing,  ^IvL,  of 
a  vertical  arm,  and  showing  the  alternate  11  inch  and  16^  inch 
similar  bearings  of  the  radius  rods  and  arms.  These  bearings 


MACHINE   CONSTRUCTION   AND   DRAWING.  167 

touch  each  other,  as  shown  from  g'  to  the  left  on  the  elevation. 
The  annular  space  between  the  circles  d!  and  f  is  fluted,  as  at 
g',  and  to  the  left,  by  the  alternate  thick  and  thin  necks,  gLK 
and  rf,  or  II  and  J,  through  which  the  arms,  E,  and  rods,  FF',  run. 
This  cannot  be  very  clearly  shown  without  shading  the  eleva- 
tion, which  may  be  done  with  fine  effect. 

The  student  may  also  usefully  add  a  central  section,  on  JF, 
and  a  cross  section  on  II,  of  the  hub. 


C— SURFACE  REGULATORS. 

After  fly-wheels,  column  five  of  the  general  table  of  elements 
of  machines  affords  no  more  examples  for  drawing  till  we  come 
to  volume  elements. 

Plane  throttle  valves  are  simply  like  a  common  stove-pipe 
damper,  a  very  rude  contrivance. 

115.  Single  poppet  valves  lift  off  of  their  seats,  instead  of 
sliding  across  them,  as  do  slide  valves,  whether  reciprocating, 
or  oscillating,  as  in  the  valves  of  a  Corliss  engine,  which  are  like 
a  door,  only  so  thick  that  its  thickness  covers  the  opening  which 
it  commands,  and  so  its  wide  cylindrical  edge  slides  on  and  off 
the  rectangular  opening  in  its  concave  cylindrical  seat. 

116.  Cage  valves,  illustrated  in  my  "  Elementary  Projection 
Drawing,"  and  so  called  from  their  name,  are  used  in  locomo- 
tive pumps,  and  perhaps  in  some  other  similar  situations,  where 
a  valve  must  act  rapidly  against  great  resistance. 

117.  Cylindrical  throttle  valves,  to  be  illustrated  by  and  by 
in  a  goveiior,  are  the  modern  improvement  over  the  old  dam- 
per throttles,  and  act  to  open  a  series  of  retangnlar  openings  at 
once,  which,  when  fully  open,  give  an  area  of  opening  equal 
to  that  of  the  pipe  which  they  command. 

118.  Ball  valves  are  simply  balls  fitting  a  spherical  seat. 
They  were  formerly  used  instead  of  cage  valve,  in  which  the 
valve  is  a  cylindrical  cup  with  a  flat  seat. 


D— VOLUME  REGULATORS. 

119.  Cocks  are  named  from  the  number  of  passages  which 
they  control,  and  consist  essentially  of  a  perforated  conical 
stem,  turning  about  its  axis  in  its  conical  seat,  whose  walls  are 


168  ELEMENTS    OF 

also  perforated.     When  the  perforations  coincide,  a  passage  is 
formed.    When  they  do  not,  it  is  destroyed. 


120.  In  globe  valves,  so-called  from  the  partly  spherical  case 
in  which  the  valve  operates,  the  latter  is  conical,  and  lifts  off 
its   seat  which   connects  two  curtains,  each  of  which  cuts  off 
half  of  the  passage ;    so  that  the  latter,   when  the  valve   is 
fully  open,  is  quite  circuitous  and  obstructed.     Still  the  globe 
valve  has   advocates,  on  account  of    an  alleged  difficulty  in 
tightly  seating  a  flat  gate  without  leaking,  dislocation,  or  grind- 
ing friction  in  unseating. 

121.  Water  gates,  used  also  for  steam  and  gas,  are  very  per- 
fect in  theory,  and  highly  esteemed  in  practice.     Two  of  the 
best,  are  made  at  Troy,  New  York.     In  one,  the  Ludlow  valve, 
Figs.  49,  50,  the  gate  is  seated  by  the  wedging  action  of  an  in- 
clined plane  at  its  back,  with  an  ingenious  arrangement  for 
loosening  the  valve  from  its  seat  before  it  begins  to  be  drawn 
off  the  same. 

A  vertical  section  of  the  apparatus  is  shown  in  Fig.  49.  A 
is  the  valve  box,  through  which  the  water  flows  from  right  to 
left  or  left  to  right.  B  is  the  valve  or  gate,  ground  to  fit  its 
face,  oo.  The  rear  of  the  valve  box  is  formed  with  two  wedge- 
shaped  projections,  del,  shown  in  perspective  in  Fig.  50.  Be- 
tween these  projections  and  the  valve,  is  the  wedge,  E,  the  ridge 
on  its  face  pressing  against  the  back  of  the  valve.  B.  The  valve 
stem  raises  and  lowers  the  wedge,  and  through  this,  only,  acts 


MACHINE    CONSTRUCTION    AND    DRAWING. 


169 


upon  the  valve.  Upon  the  back  of  the  valve  is  formed  a  Ing, 
h,  which  enters,  loosely,  a  circular  recess  in  the  wedge,  and  by 
this  arrangement  the  wedge  is  permitted  to  move  upward  a  cer- 
tain distance,  thus  loosening  the  valve  before  it  begins  to  rise. 
Whatever  the  position  of  the  apparatus,  the  wedge  cannot  pinch 
the  gate  before  the  valve  opening  is  covered. 

In  the  Brown  valve,  Fig.  51,  the 
valve,  V,  is  fastened  by  a  brace,  a, 
acting  somewhat  after  the  manner 
of  a  toggle  joint,  rising  and  falling 
with  the  valve,  in  standing  guides, 
see  the  figures.  It  acts  with  very 
little,  if  any,  injurious  sliding  un- 
der pressure  between  the  valve 
and  the  seat,  owing  to  the  roller 
form  of  the  ends  of  the  brace. 

In  all  of  the  last  three  contri 
vances,  the  effectual  packing  of  the 
valve  stem,  which  should  work  in 
a  tight  collar,  especially  for  steam 
and  gas,  is  a  matter  still  deserving 
of  attention. 

All  such  devices  as  these,  al- 
though practically  very  important, 

are  hardly  elements  of  machines  in  such  a  sense  as  to  afford 
examples  for  full  illustration,  unless,  as  in  the  following  cases, 
on  account  of  their  ingenuity,  novelty,  or  grand  importance. 


EXAMPLE  XLII. 

Chambered  or  'D'  Locomotive  slide  valves  ;  Plain  and  Anti- 
friction. 

Description. — The  common  slide  valve,  PI.  IY.,  Fig.  2,  is  best 
understood  in  connection  with  the  cylinder.  T,T',T"  is  its  hol- 
low interior,  which  is  sufficient  to  cover  the  exhaust  port,  bd, 
and  either  one  of  the  steam  ports,  as  ce. 

From  the  shape  of  the  section,  T",  of  the  valve,  it  is  often 
called  a  D  valve,  cd — c"d" — c'd'pq  is  the  rectangular  yoke,  sur- 
rounding the  body  of  the  valve,  and  forged  to  the  valve  stem,  $, 
by  which  the  valve  is  actuated,  baa" — a'  is  one  of  two  stiffening 


170  ELEMENTS    OF 

ribs  on  top  of  the  valve,  shown  in  plan  in  dotted  lines,  the 
valve  being  there  upside  down. 

The  valve  is  shown  raised  from  its  seat,  gt,  Fig.  1,  and  out  of 
position  relative  to  the  piston.  Supposing  the  latter  to  be  just 
about  to  begin  its  stroke  to  the  left,  the  valve  should  be  far 
enough  to  the  left  to  have  opened  the  steam  port,  ce,  already, 
about  one-eighth  of  an  inch.  This  distance  is  called  the  lead 
of  the  valve,  and  it  serves  to  admit  live  steam  a  little  before  the 
beginning  of  the  stroke ;  which  cushions  the  piston,  and  re- 
lieves it  from  the  jerking  strain  of  a  very  sudden  change  of 
motion. 

The  difference  between  the  width  of  the  lip  or  face,/$,  of 
the  valve,  and  the  port,  ce,  is  called  the  lap  of  the  valve.  Its 
amount,  in  this  case  1  inch,  determines  the  point  in  the  piston 
stroke  at  which  steam  is  cut  off ;  as  will  be  more  fully  explained 
by  and  by. 

The  minute  recesses,  as  m  and  n,  which  break  joints  with 
each  other,  serve  to  secure  a  lubrication  of  the  valve  seat  by  the 
steam. 

In  contrast  with  the  common  slide  valve,  the  friction  of  which 
is  very  great,  PI.  XXIY.,  Fig.  3,  represents  a  frictionless  slide 
valve,  wThich  is  believed  to  accomplish  the  purpose  of  saving 
the  wear  on  the  valve  seats,  eccentrics  and  other  gear,  caused 
by  the  excessive  friction  inherent-  in  all  sliding  valves. 

This  valve  is  not  of  the  balanced  valve  variety,  which,  for 
locomotives,  has  been  thought  to  be  impracticable,  but,  as  seen  by 
the  figure,  it  works  by  changing  a  rubbing  to  a  rolling  friction. 
When  the  valve  is  in  operation,  it  is  so  suspended  from  the 
axles  of  the  rolls  R,R,  by  means  of  saddle  plates  SS,  that  it 
works  just  in  steam  tight  contact  with  the  seat  AA,  without  any 
appreciable  friction  as  the  valve  moves  back  and  forth ;  for  the 
pressure  comes  upon  the  axles,  BB,  through  the  saddle  plates, 
and  so  causes  the  rollers  to  roll  upon  the  ways  CO.  In  this 
movement  of  the  rollers  and  axles,  there  is,  however,  no  rubbing 
friction,  as  not  only  is  the  friction  of  the  rollers  upon  the  ways 
of  the  rolling  kind,  but  so  is  the  friction  of  the  axles  on  the 
saddle  plates,  and  hence  there  is  no  appreciable  resistance  what- 
ever to  the  movement  of  the  valve  created  by  the  pressure  of 
steam  on  the  back  of  it.  The  rolls,  axles,  ways,  and  saddle 
plates,  are  of  hardened  steel,  and  subject  to  a  crushing,  not  a 
rubbing  force.  It  is  said,  that  after  a  test  of  several  years  in 


MACHINE    CONSTRUCTION  AND   DRAWING. 


171 


different  engines,  valves  so  applied,  do  not  show  the  least  indi- 
cation of  wear. 

These  valves  are  in  use  in  locomotives  on  a  number  of  the 
leading  railroads  of  the  United  States,  and  can  be  put  on  any 
locomotive  in  a  few  hours'  time. 

Construction. — As  there  is  a  considerable  difference  in  the 
size  of  the  ports  in  different  engines,  the  student  can  readily 
assume  these,  and  then  draw  the  valve,  either  in  plan  and  ele- 
vations, or  in  isometrical  or  oblique  projection,  from  suitable 
measurements. 

EXAMPLE  XLIII. 
Tremairfs  Balanced  Piston   Valve. 

Description. — The  valve  of  the  stearn  engine  has  probably 
been  the  subject  of  more  thought  than  any  other  piece  of 


mechanism  of  equal  size  and  simplicity.  The  great  amount  of 
power  absorbed  in  working  it,  the  strength  and  weight  conse- 
quently required  in  all  the  parts  connected  with  it,  the  constant 
wear  and  liability  to  break  down,  the  delay  and  expense  of 


172 

repairs,  the  difficulty  of  reversing  or  working  the  valves  of 
large  engines  by  hand,  are  sufficiently  well  known.  The  object 
has  been  to  relieve  the  common  slide  valve  of  the  pressure  of 
steam,  and  many  ingenious  contrivances  have  been  invented  f  or 
this  purpose.  This  has  been  accomplished  by  the  invention 
here  illustrated.  This  balanced  slide  valve  is  of  the  piston 
variety,  and  its  claims  to  superiority  are  of  a  novel  character, 
and  such  as  to  attract  the  attention  of  engineers  and  owners  of 
steam  engines. 

First,  it  is  a  perfectly  balanced  valve ;  it  requires  no  adjust- 
ment; it  is  simple  and  not  liable  to  get  out  of  order.  The 
cost  of  its  application  to  engines  now  used  is  small,  while  for 


new  engines,  the  redaction  effected  in  the  weight  of  all  the 
valve-gear  makes  it  much  cheaper  than  the  common  valve.  It 
is  applicable  to  either  high  or  low  pressure  engines,  or  when 
single  valves  at  each  end  of  the  cylinder  are  used.  By  it  a  much 
longer  port  is  obtained  than  by  the  common  slide  valve.  In  a 
steam  chest  eight  inches  in  diameter,  the  circumference  being 


MACHINE    CONSTRUCTION    AND   DRAWING.  173 

over  twenty-five  inches,  the  steam   port  will  be  twenty-one 


inches.     This  is  of  very  great  advantage  in  clearing  the  cylin- 
der of  steam  after  it  has  done  its  work. 


174 


ELEMENTS    OF 


FIG.  56. 


Fig.  52  is  a  longitudinal  section,  showing  the  application  to 
old  engines  now  in  use.  The  same  letters  refer  to  like  parts. 
Fig.  53  is  an  end  view  of  Fig.  52,  showing  the  bolts,  D,D,  in 
dotted  lines.  Fig.  54  shows  the  manner  of  bolting  the  chest  on, 


MACHINE   CONSTRUCTION   AND   DRAWING.  175 

when  it  is  not  convenient  to  cast  it  and  the  cylinder  together. 
Fig.  55,  valve  heads  connected  by  common  pipe  when  the  cylin- 
der is  long.  Fig.  56,  valve  showing  guide,  S,  and  the  way  the 
i-ings,  R,  are  set  out ;  these  rings,  R,  being  in  three  parallel 
parts,  prevent  leakage  of  steam  by  breaking  joints ;  while  the 
manner  in  which  they  are  set  out  is  adapted  to  prevent 
leakage  by  their  being  compressed  inward  by  the  steam.  Fig. 
57  is  an  end  view  with  steam  chest  cast  on  the  cylinder. 

The  valve  is  placed  in  the  cylindrical  steam  chest,  which  has 
two  grooves,  AA,  encircling  it,  which  are  in  communication  with 
the  steam  ports,  A,  which  lead  into  the  cylinder,  L.  Steam  is 
admitted  through  the  side  pipe,  J.  The  grooves,  A,A,  are 
covered  by  the  ring,  B,  which  forms  the  valve  seat  and  contains 
the  ports,  p,p,  through  which  steam  passes  into  and  out  of  the 
cylinder,  L.  E  is  the  opening  for  exhausting  the  steam  from 
the  cylinder.  The  valve,  C,  is  hollow,  and  is  secured  upon  the 
stem,  G.  The  rings,  R,  are  secured  by  the  follower,  I,  which 
is  recessed  into  the  ring  and  will  not  come  in  contact  with  the 
seat,  B.  DD  are  bolts  by  which  the  chest  is  fastened  to  engines 
previously  using  the  common  slide  valve. 

Construction. — Let  the  figures  be  arranged,  with  the  different 
elevations  of  the  same  thing  on  the  same  level. 


EXAMPLE  XLIY. 
^Balanced  Poppet  Valves. 

Description. — In  marine  engines  of  comparatively  short  and 
quick  stroke,  as  propeller  engines,  slide  valves,  like  those  of 
locomotives,  but  of  proportionally  larger  size,  are  frequently 
used ;  while  for  engines  of  long  and  slow  stroke,  like  beam 
engines  generally,  poppet  valves  are  used. 

A  poppet  valve  lifts  off  from  its  seat,  and  a  balanced  poppet- 
valve,  PL  XXV.,  Fig.  1,  where  one-half  of  a  valve  is  shown  at 
AIIB,  has  two  seats,  CD  and  cd.  These,  like  the  valve,  are  cir- 
cular in  plan,  the  figure  being  a  vertical  section ;  and  as  steam 
enters  from  the  steam  pipe  S,  as  shown  by  the  arrows,  the 
pressure  downward  of  the  steam  at  CD  resists  the  opening  of 
the  valve,  while  the  upward  pressure  at  cd  assists  its  opening. 
Hence,  by  making  the  diameter  of  the  upper  opening  one  inch 


176  ELEMENTS   OF 

greater  than  that  of  the  lower  one,  the  valve  is  lifted  only  against 
the  downward  pressure  on  a  ring  of  half  an  inch  in  width,  and, 
in  this  case,  23f  inches  outside  diameter. 

E/TJ  is  a  vertical  section  of  the  steam  chest  of  a  marine  berrn 
engine  built  by  the  Novelty  TVorks  for  the  Pacific  Mail  Co., 
and  with  a  cylinder  105  inches  diameter,  and  12  feet  strike. 
S  is  the  steam  pipe  (see  also  PI.  Y.,  Figs.  5,  6),  bolted  at  EF  to 
the  vertical  pipe  leading  to  a  similar  chest  at  the  top  of  the 
cylinder.  Steam  flowing  into  the  spaces,  KK,  rushes  through 
the  openings  made  by  the  lifting  of  the  steam  valve  AIIB ; 
through  the  steam  port,  LL,  into  the  bottom  of  the  cylinder,  and 
forces  up  the  piston. 

At  the  same  time,  the  upper  exhaust  valve,  corresponding  to 
ahb,  lifts,  and  sets  free  the  steam  which  effected  the  previous 
stroke,  and  which  then  escapes  through  the  exhaust  pipe.  This 
pipe  is  bolted  on  at  ef,  and  the  steam  thus  passes  on  through  G 
and  the  exhaust  port,  MM,  to  the  condenser. 

Again,  when  the  upward  stroke  is  just  about  to  end,  the  upper 
steam  valve,  corresponding  to  AIIB,  lifts  and  admits  steam  to 
"  cushion  "  the  piston  at  the  end  of  its  upward  stroke,  and  drive 
it  down  again,  while  the  lower  exhaust  valve,  aJib,  opens  and 
steam  flows  out  of  LL  into  G,  and  through  M  to  the  condenser. 
The  partitions  NX  divide  the  steam,  from  the  exhaust  chamber. 
It  is  thus  seen  that  live  and  exhaust  steam  can  never  meet  un- 
less, as  in  LL,  by  the  two  valves  AIIB  and  ahh,  being  both  open 
at  once  for  a  moment. 

The  valves  are  circular,  as  seen  in  plan,  and  therefore  suffi- 
ciently shown  in  the  plate,  by  a  half  vertical  section  of  each. 
Each  valve  is  keyed,  as  at  fek',  to  a  vertical  valve  stem.  The 
latter  are  connected  by  short  horizontal  arms  to  the  vertical 
lifting  rods,  as  Y,  Fig.  4,  in  front  of  the  cylinder.  These  rods 
are  lifted  by  wipers,  "W,  keyed  to  an  oscillating  rock-shaft,  U, 
which  is  operated  by  an  eccentric  on  the  main  shaft ;  whose  rod, 
E,  takes  hold  of  the  free  end  of  a  rocker-arm,  A,  keyed  to  the 
rock-shaft.  The  wipers,  W,  act  upon  toes,  T,  keyed  to  the 
lifting-rods,  Y. 

The  form  of  the  upper  surface  of  the  wiper  and  its  angular 
position  on  the  rock-shaft,  together  with  the  position  of  the 
eccentric,  determine  the  height  and  rapidity  of  the  lift  of  the 
valve,  and  the  points  in  the  piston  stroke  at  which  it  will  open 
and  close.  By  opening  the  steam  valves  just  before  the  end  of 


MACHINE   CONSTRUCTION   AND   DRAWING.  177 

a  piston  stroke,  the  piston  is  cushioned,  so  as  to  ease  the  shock 
of  the  sudden  reversal  of  the  motion  of  its  heavy  mass.  By 
closing  them  at  or  soon  after  the  middle  of  the  stroke,  the  ben- 
efit of  the  expansive  use  of  the  steam  is  obtained. 

To  avoid  back  pressure  on  the  advancing  face  of  the  piston, 
the  exhaust  valves  are  larger,  or  are  lifted  higher,  and  held  open 
longer  than  the  steam  valves ;  as  may  be  seen  by  watching  the 
different  motions  of  their  two  lifting-rods  on  any  river-boat 
engine.  This  result  is  effected  by  making  their  toes  shorter, 
while  their  wipers  begin  to  act  at  a  point  nearer  the  rock-shaft 
than  is  the  case  with  the  steam-valve  wipers. 

To  enter  minutely  into  this,  and  closely  kindred  subjects,  with 
their  theory,  might  occupy  a  small  volume  ;  hence  this  descrip- 
tion closes  with  the  following  data  from  actual  practice. 

First,  in  the  Pacific  Mail  Steamers. 

Steam  pressure  in  boiler 18  Ibs. 

Mean  pressure  in  cylinder Depends  on  point  of  cut-off. 

Diameter  of  cylinder 105  ins. 

Length  of  stroke 12  feet. 

Steam  cut-off  at 2|  to  6  feet. 

Steam  valve  opening  at  beginning  of  stroke  =  lead =-pg  ins. 

Height  to  which  steam  valve  is  Iifted=i7£  ins. 

Exhaust  valve  opening  at  beginning  of  stroke = exhaust  lead  or  retease=2$  ins. 

Height  to  which  it  is  lifted=7$  ins. 

The  following  data  are  from  the  engines  of  the  remarkable 
shore  steamers  "  Providence  "  and  "Bristol,"  and  were  furnished 
by  Mr.  Thomas  Main,  Eng.,  their  designer  for  the  Messrs. 
Roach,  their  builders  : — 

1.     Steam  pressure  in  boiler,  above  atmosphere . .  21  Ibs. 

o    (  Diameter  of  cylinder 110  ins. 

(  Of  side  pipes 30  ins. 

3.     Length  of  stroke 12ft. 

4     Usual  point  of  cut-off 5  ft. 

5.  Mean  pressure  in  cylinder,  about 25  Ibs. 

6.  Lead  of  steam  (poppet)  valve ~uf  to  ^  ins. 

7.  Total  lift  of  steam  valve 5*  ins. 

8.  Diameters  of  do 20  and  21  ins. 

9.  Lead  of  exhaust  valves 2^  ins. 

10.  Total  lift  of  do 7  ins. 

11.  Diameters  of  do 21  and  22  ins. 

12.  Three  boilers,  each 35  ft.  long  by  12  ft.  5  ins.  diar 

13.  Grate  surface 510  sq.  ft. 

14.  Fire  surface 13,850  sq.  ft. 

12 


178 


ELEMENTS   OF 


15.  Surface  condenser.     Surface 4,500  sq.  ft. 

16.  Paddle-wheels,  38  ft.  8  ins.  diameter,  12  ft.  face.     Paddles  "  stepped  ! 

thus  j-      I  to  prevent  jar. 


MACHINE   CONSTRUCTION    AND   DRAWING.  179 

Steamship    "  Providence. " 

•Date April  30th,  1869. 

Which  end  of  cylinder Both. 

Revolutions  per  minute 17|. 

Pressure  of  steam  in  boilers,  in  Ibs  21. 

Point  of  cut-off 5  ft. 

Position  of  throttle- valve Open. 

Vacuum  per  gauge,  in  inches 26. 

Temperature  of  hot  well,  Fahrenheit 122°. 

Scale  of  indicator,  16  Ibs.  to  an  inch. 

Construction. — The  student  can  show  the  whole  of  each 
valve  and  a  plan  of  one,  and  the  scale  for  the  steam-chest 
being  reduced  from  -^  to  -£%,  or  even  to  T^,  the  valves  may  be 
shown  separately  on  a  scale  of  from  one-fourth  to  one-eighth, 
with  enlarged  sections  at  the  seat,  as  in  Figs.  2  and  3. 

122.  The  general  view,  Fig.  58,  will  make  the  above  example 
more  intelligible. 

G,  is  the  heavy  supporting  frame  of  the  whole  engine,  and 
called  the  gallows  frame;  C,  is  the  steam  cylinder;  B,  the 
working  beam ;  BE,  the  connecting  rod ;  R5,  the  crank,  turn- 
ing the  main  shaft,  in  the  pillow-block  l>.  A,  is  the  air-pump ; 
F,  a  force-pump  for  supplying  water  to  the  surface  condenser, 
S  (PI.  V.),  through  passages  in  the  bed-plate,  P  (PI.  YIIL).  W, 
is  one  of  the  paddle-wheels ;  V,  is  the  steam,  or  valve-chest,  r 
and  r  are  the  rocker-arms,  see  A,  PI.  XXV.,  Fig.  4,  the  pins  of 
which  are  engaged  by  the  eccentric  hooks.  The  rock-shaft,  rr, 
is  in  two  parts,  which  meet  at  a  common  central  bearing.  One 
eccentric  is  for  the  steam,  and  the  other  for  the  exhaust  valves. 
The  former  has  a  large  throw  so  as  to  actuate  its  rocker  through 
a  large  arc,  and  quickly.  A  long  and  adjustable  wiper  on  its 
rock-shaft,  acting  on  the  toe,  T,  PL  XXV.,  only  during  a  part 
of  its  arc,  raises  that  toe  with  the  steam  valve  quickly,  and 
closes  it  at  a  point  in  the  stroke,  depending  on  the  angular 
position  at  which  the  wiper  is  set  on  the  rock-shaft. 

123.  The  following  abstracts  from  observations  at  sea  are  in- 
teresting, as  showing   the  relation  of  cut-off  to  cylinder  and 
boiler  pressures : 

1°.  Steamship  "  Montana." 

Which  engine,  main.  Which  end  of  cyl.,  top  and  bot.      Rev'ns  $  min.,  9. 

Throttle,  wide.  Steam,  18  Ibs.  Vacuum,  27  ins. 

Sea  water  tern' re.  63°.  Discharge  water  tem're,  70°.  Feed  water  tem're,  120°. 

Engine  room  tem're,  70".  Cut-off,  2  ft.  Coal  $  hour,  2,536  Ibs. 

Initial  cylinder  pressure,  top,  13.8  Ibs.,  bottom,  13.9  Ibs. 


180  •  ELEMENTS   OF 

2°.  Steamship  "  Montana." 

Which  engine,  main.  Which,  end  of  cyl.,  top  and  hot.      Rev'ns  $  min.,  9. 

Throttle,  wide.  Steam,  20  Ibs.  Vacuum,  27  ins. 

Sea  water  tem're,  80°.  Discharge  water  tem're,  90°.  Feed  water  tem're,  120°. 

Engine  room  tem're,  86°.  Cut-off,  2  ft.  6  ins.  Coal  $  hour,  2,614  Ibs. 

Initial  cylinder  pressure,  top,  17.1  Ibs.,  bottom,  17.5  Ibs. 

3°.  Steamship  "  Montana." 

Which  engine,  main.  Which  end  of  cyl.,  top  and  hot.      Rev'ns  $  min.,  7.8. 

Throttle,  #  open.  Steam,  21  Ibs.  Vacuum,  27  ins. 

Sea  water  tem're,  88°.  Discharge  water  tem're,  94°.  Feed  water  tem're,  120°. 

Engine  room  tem're,  86°.  Cut-off,  8  ft.  Coal  $  hour,  2,800. 

Strong  head-wind  and  sea. 

Initial  cylinder  pressure,  top,  18.9  Ibs..  bottom,  19.3  Ibs. 

4°.  Steamship  "  Montana." 

Which  engine,  main.  Which  end  of  cyl.,  top  and  bot.       Rev'ns  ff  min.,  8. 

Throttle,  wide.  Steam,  21  Ibs.  Vacuum,  27  ins. 

Sea  water  tem're,  84".  Discharge  water  tern're,  90°.  Feed  water  tem're,  120°. 

Engine  rooom  tem're,  86°.          Cut-off,  3  ft.  6  ins.  Coal  $  hour,  2,925. 

Initial  cylinder  pressure,  top.  20.5  Ibs.,  bottom,  21  Ibs. 

The  increasing  difference  between  boiler  and  cylinder  pres- 
sure as  the  cut-off  takes  place  earlier,  indicates  the  increased 
wire  drawing  of  the  steam,  as  the  steam  valves  are  less  lifted 
and  quicker  closed. 

The  difference  between  the  sea-water  temperature  and  the 
discharge-water  temperature  shows  how  much  the  sea  water  is 
heated  in  passing  through  the  condenser  tubes. 

The  increase  of  fuel  required  to  maintain  the  boiler  pressure 
as  the  cut-off  is  later,  is  also  noticeable. 


EXAMPLE  XLY. 
Richardson's  Locomotive  and  Lock-up  Safety   Valve. 

Description. — Fig.  59  represents  the  form  of  this  valve,  as 
applied  to  locomotives,  on  a  scale  of  one-half. 

AA,  represents  a  section  of  an  ordinary  dome  cap  or  plate, 
with  the  projecting  lip  or  flange  a,  which  may  be  cast  on,  and 
form  a  part  of  the  valve  seat  B  ;  or  it  may  be  formed  by  letting 
the  bush,  B,  down  into  the  dome  cap. 

BB,  is  a  section  of  a  brass  bush,  on  which  is  formed  the 
valve  seat,  KK,  which  should  be  bored  with  a  spherical  rose 
cutter,  having  a  If-inch  radius. 

CO,  is  a  section  of  a  four-winged  valve  with  chamber  c" 
formed  by  a  lip  projecting  ^gth  of  an  inch  beyond  and  drop- 
ping ^g-th  of  an  inch  below  the  top  of  the  bush  B. 


MACHINE    CONSTRUCTION    AND    DRAWING. 


181 


DD,  is  a  steel  spindle,  with  the  plate  E  shrunk  on,  and 
turned  true.  That  portion  of  E  indicated  by  the  dotted  line 
should  fit  closely  within  the  spring.  Th«  spindle  should  bear 
on  its  point,  d,  and  be  ^th  of  an  inch  loose  in  the  bore.  The 
upper  end  of  the  spindle  passes  through  the  cross-head,  G,  ^th 
of  an  inch  loose,  which  keeps  it  in  a  central  position,  at  the 
same  time  allowing  it  to  move  freely  up  and  down. 

FF,  is  a  helical  spring,  supported  by  the  plate  E,  and  bear- 
ing against  the  cross-head  G.  This  spring  is  formed  of  a  bar  of 


182  ELEMENTS    OF 

f-inch  cast  steel,  40£  inches  long,  with  the  ends  tapered  3 
inches,  and  when  coiled,  faced  off  at  both  ends  and  tempered. 

GG,  is  the  cross-head,  made  of  hard  brass,  and  adjusted  by 
the  nuts  II  on  the  studs  HII,  which  are  screwed  into  the  dome 
cap  AA. 

JJ,  is  a  section  of  a  washer  fitting  closely  to  the  spindle,  but 
moving  freely  thereon,  for  the  purpose  of  keeping  the  sparks  or 
cinders  from  filling  up  the  space  surrounding  it. 

The  cut  may  be  regarded  as  a  working  drawing  for  a  2J-inch 
valve  (the  locomotive  size),  in  which  the  spring  is  represented 
as  uncompressed.  For  100  pounds  pressure  the  spring  should 
be  screwed  down  f ths  of  an  inch,  and  proportionately  for  any 
other  pressure.  In  setting  this  valve,  the  steam  gauge  should 
be  known  to  be  accurate,  and  the  connecting  pipe  clear.  The 
cross-bar,  GG,  may  be  of  any  length  which  circumstances  shall 
require  ;  but  the  hole  through  which  the  spindle  passes  should 
line  accurately  with  the  bore  in  the  bush.  Should  the  pressure 
be  reduced  too  much  before  the  valve  closes,  increase  the  out- 
let from  c"  to  c'  by  turning  out  the  lip  of  the  valve  a  very 
little;  which  relieves  the  upward  presure  in  c" '. 

It  is  now  evident  that,  as  soon  as  the  steam  pressure  exceeds 
what  is  intended,  it  will  start  the  valve  from  its  seat,  and  then 
it  has  a  surface  of  the  larger  diameter  nearly  equal  to  LL,  to  act 
upon.  Thus  the  additional  force  necessary  to  overcome  the  in- 
creased resistance  of  the  spring  as  it  is  lifted  is  obtained,  and  a 
free  escape  for  the  surplus  steam  is  secured. 

Fig.  60  represents  the  lock-up  valve  for  stationary  and  steam- 
boat boilers.  The  same  is  shown  to  scale  in  PL  XXIY.,  Fig. 
4,  where  the  plan  shows  half  of  the  valve  case  cover,  CO', 
and  the  whole  of  the  nut  cover,  D',  removed.  The  elevation  is 
half  in  vertical  section.  Like  letters  refer  to  like  parts  on  all 
the  figures. 

A,  A/  is  the  inlet  from  the  boiler.  B  is  the  valve,  winged,  as 
at  5,^',  with  four  wings,  and  resting  on  its  seat  at  the  top  of 
the  bush  c,c',  and  enclosing  the  spindle  d,df.  S,S'  is  a  thin 
screw,  by  which  the  spring  E,E'  is  compressed  to  the  intended 
pressure.  Steam,  lifting  the  valve  by  compressing  the  spring 
from  below,  escapes  into  the  space  F,F',  and  thence  through  an 
outlet  pipe,  carried  from  GG'  to  any  convenient  point  of  dis- 
charge. A  padlock  being  locked  into  the  staple  aa',  cuts  off 
access  to  the  nuts  nri ',  which  hold  down  the  valve  case  cover 


MACHINE   CONSTRUCTION   AND   DEAWING. 


183 


CO',  and  thus  prevents  tampering  with  the  valve.  A  hand 
lever,  K,  allows  the  valve  to  be  lifted  by  hand,  if  need  be,  to  as- 
certain whether  it  has  become  stuck  to  its  seat. 

Construction. — From  Fig.  59,  a  plan  view  can  be  made,  by 
assuming  only  a  few  of  the  measurements.  And  by  careful 
comparison  of  the  two  projections  of  PL  XXIV.,  Fig.  4,  with 
Fig.  60  to  serve  in  place  of  a  model,  an  elevation  or  section 
looking  in  the  direction  of  the  arrow, p*  may  be  made. 

The  lock-up  valve  is  made  of  various  sizes ;  hence,  as  PL 
XXIV.,  Fig.  4,  is  drawn  to  scale,  to  show  its  proportions, 
measurements  may  be  assigned  to  it,  according  to  any  suitable 
scale,  so  as  to  make  the  student's  drawing  larger  or  smaller 
than  this  one. 

EXAMPLE  XLVI. 
A  Double-Beat  Pump   Valve. 

Description. — PL  XXX.,  Fig.  2,  represents  such  a  valve. 
Before  describing  the  valve  itself,  its  place  in  the  pump  should 


184:  ELEMENTS    OF 

be  understood,  and  the  nature  of  its  action  and  relation  to  ad- 
jacent parts. 

The  magnitude  of  the  great  pumping  engines  forbids  the 
use  of  any  such  valves  as  are  found  in  common  hand  pumps  ; 
and  the  necessary  size  of  single  valves  would  make  them  cum- 
brous. 

For  example,  the  cylinder  of  Brooklyn  Pumping  Engine  !S"o. 
3,  is  of  85  inches  diameter,  with  10  feet  stroke.  The  pump  is 
directly  under  the  cylinder,  of  51£  inches  diameter,  and  10 
feet  stroke.  As  the  bucket  of  this  pump  ascends,  it  lifts  the 
water  above  it,  and  the  pump  is  filled  by  water  rushing  up 
through  a  group  of  20  foot-valves,  commanding  inlets  of  11^ 
inches  diameter  each ;  arid  all  contained  in  a  chamber  of  S9-J 
inches  diameter.  On  the  down  stroke,  a  valve  of  44  inches 
diameter  opens  in  the  bucket  itself,  together  with  13  others  of 
the  size  before  given,  and  placed  around  an  annular  space  sur- 
rounding the  pump-barrel,  and  opening  into  it. 

Xow,  to  diminish  the  work  of  lifting  these  valves  in  the 
water,  they  are  made  as  in  the  figure,  where  the  annular  seats, 
E  and  F,  are  called  beats.  There  being  two  of  these,  the  valve 
is  called  a  double-beat  valve.  The  figure  is  a  plan  and  sec- 
tional elevation,  and  the  parts  shown  in  section  line  are  of  uni- 
form section  all  around  the  valve.  "Whence  it  is  plain  that  the 
valve  is  lifted  against  the  vertical  pressure  of  an  annular 
column  of  water  of  the  horizontal  width  from  c  to  e.  The 
bridges.  H,  slide  up  and  down  on  the  stem,  G.  as  a  guide.  The 
unshaded  parts  are  six  radial  arms,  or  wings,  to  stiffen  the 
valve  wall  I.  Thus  the  water  escapes,  as  shown  by  the  arrows 
e  and/! 

The  seats  E  and  F  may  be  of  wood,  or  other  like  material,  to 
avoid  heavy  concussion  in  closing  the  valves. 

Though  a  partial  digression,  it  may  be  added  that  this  double 
acting  pump  is  built  upon  what  is  called  the  fly-wheel  system. 
That  is,  at  the  opposite  end  of  the  working  beam — which  is  31 
feet  long,  and  weighs  30  tons — is  a  26  foot  fly-wheel  in  10  seg- 
ments, and  weighing  36  tons ;  on  a  shaft  20  inches  diameter. 
And  it  is  reported,  after  official  trial,  that  the  work  done  is  the 
raising  of  72,000,000  pounds,  1  foot  for  every  100  pounds  of  coal 
consumed,  which  is  equivalent  to  81,000,000  pounds  raised  1  foot 
by  112  pounds  of  coal,  the  standard  of  fuel  weight  given  in 
some  English  authorities. 


MACHINE   CONSTRUCTION   AND   DRAWING.  185 

This  engine  is  reported  as  doing  about  double  the  duty  in 
proportion  to  the  fuel,  that  is  done  by  engines  Nos.  1  and  2, 
each  having  a  force  pump  at  each  end  of  the  beam,  and  no  fly- 
wheel. The  celebrated  Cornish  engines  are  without  fly-wheels, 
and  have  a  steam  cylinder  at  one  end  of  the  beam  and  the 
pump  at  the  other,  with  the  pump-end  of  the  beam  shorter 
than  the  other. 

We  cannot  enter  into  the  discussion  of  the  relative  merits  of 
these  and  other  forms  of  pumping  engines,  but  must  refer  the 
reader  to  the  Jour.  Franklin  Institute  for  1868-69-70,  Bourne's 
works  on  the  steam  engine,  etc. 

It  seems  probable  that  the  marvellous  duty  of  100  to  120 
million  pounds  raised  1  foot,  per  100  pounds  of  coal  burned, 
attributed  to  the  Cornish  engines,  may  be  partly,  at  least, 
owing  to  the  fact  that  their  construction,  with  suitable  boilers 
also,  has  been  made  a  specialty  for  many  years,  under  every 
stimulus  of  necessity  for  economical  results,  that  could  well  exist. 

Construction. — As  the  many  dotted  circles  in  the  plan  are 
hardly  intelligible  before  a  careful  tracing  out  of  their  vertical 
projections,  the  student  should,  as  a  study,  draw  this  valve  on  a 
scale  of  one-fourth,  or  even  Q\\Q-hcdf,  and  then  add  the  tangent 
projecting  lines  of  every  circle  of  the  plan. 

EXAMPLE  XLVIL 
The   Cornish  Equilibrium   Valve. 

Description. — This  is  a  steam  valve,  used  on  the  Cornish 
engines  already  referred  to.  Its  conical  seats  are  mn  and  op, 
on  which  rest  the  corresponding  edges  MIS"  and  OP,  of  the 
valve  when  that  is  seated.  Otherwise,  the  figure  explains  itself. 

Construction. — The  horizontal  section  shows  in  section  lines 
the  radial  supports  of  the  valve  wall.  See  also  the  directions 
in  the  last  problem. 

EXAMPLE  XLYIII. 
Giffartfs  Injector. 

Description. — This,  as  well  as  the  last  device  described,  is 
rather  an  instrument  (30)  than  a  machine,  as  its  moving  parts 


186  ELEMENTS    OF 

are  separately  adjustable,  yet  as  it  is  not  used  separately,  but  as 
an  accessory  to  the  steam  engine,  we  make  a  place  for  it. 

Giffard's  Injector,  PI.  XXIV.,  Fig.  5,  is  a  contrivance  for 
making  the  steam  power  in  a  boiler,  feed  the  boiler  with  water, 
by  means  of  the  work  developed  by  the  rush  of  the  steam  to- 
wards the  vacuum  constantly  tending  to  form  where  the  steam 
is  condensed  by  contact  with  the  cold  water  supply ;  that  is, 
ultimately,  by  the  conversion  of  the  heat  of  the  steam  into  its 
equivalent  in  mechanical  force  at  that  point. 

We  will,  before  explaining  the  action  of  the  injector,  give  a 
general  description  of  the  apparatus  as  improved  and  made  by 
William  Sellers  &  Co.  It  is  in  two  parts,  joined  at  ee  by  bolts 
dd.  AA  is  the  steam  inlet,  separated  from  the  water  inlet  K 
by  the  parti ti on  ff.  BB,  a  screwed  rod,  operated  by  the  winch 
«,  and  which,  by  rising  and  lowering  through  the  nut  n,  adjusts 
the  opening  at  C,  and  hence  the  flow  of  steam  to  form  the  jet. 
B  is  hollow  and  perforated,  so  that  a  little  steam  will  flow 
through  it,  even  when  closed  down.  D  is  a  tube,  combined 
with  a  piston,  FF,  which  slides  in  the  space  F£,  as  actuated  by 
the  overflow  of  excess  of  water  at  E.  The  delivery  tube,  G,  is 
attached  to,  and  moves  with  FD,  the  piston  tube.  H  is  the 
waste  valve  operating  in  the  small  space  at  c,  and  allows  any 
overflow  from  G  to  escape.  This  valve  is  sometimes  opened 
laterally  by  hand,  acting  on  a  screw  stem  through  H.  J  is  the 
foot  valve,  here  shown  wide  open ;  and  which,  when  closed, 
prevents  the  return  of  water  from  the  boiler,  when  the  injector 
is  not  working.  L  is  the  outlet  to  the  boiler.  The  pipes  con- 
necting at  A,  K,  and  L  should  be  of  the  same  diameter  as  those 
apertures,  and  as  short  and  straight  as  possible.  Steam  is  let 
on  by  a  cock  in  the  pipe  entering  at  A ;  and  there  should 
be  a  regulating  cock  in  the  water  pipe  entering  at  K,  in  case 
the  water  flows  in  under  pressure  as  from  a  level  above  the 
injector,  instead  of  being  lifted  from  below,  as  is  often  done. 

Operation. — Screw  down  the  plug  B  to  its  lowest  point,  when 
steam  issuing  through  the  small  perforation  in  it,  before  described, 
and  from  its  point,  will  act  to  produce  a  vacuum  about  D, 
which  will  draw  water  in,  as  by  "  suction,"  at  Iv,  and  force  it 
along  to  II  and  out  at  I,  the  valve  J  being  closed  by  the  boiler 
pressure.  The  screw  plug  B  being  then  drawn  outward,  the  flow 
of  steam  will  increase  until  the  force  of  the  combined  steam  and 
water  current  opens  J,  and  proceeds  on  into  the  boiler.  If  now 


MACHINE   CONSTRUCTION   AND   DRAWING.  187 

the  water  supply  be  too  great,  there  will  be  an  overflow  at  E, 
which  will  accumulate  in  NN,  and  drive  back  the  piston  tube 
FFD,  and  thus  narrow  the  water  entrance;  see  the  arrow  at 
D,  and  properly  reduce  the  water  supply.  But  if  the  water 
supply  be  relatively  too  small,  the  freer  rush  of  steam  through 
the  nozzle  AC,  will  produce  a  partial  vacuum , around  C,  into 
which,  water  flowing  more  forcibly,  will  drive  back  FFB,  and 
enter  more  abundantly.  This  self -regulating  feature  is  of  great 
value  by  dispensing  with  frequent  regulations,  by  hand,  of  the 
relative  steam  and  water  supplies  which  are  oftener  required, 
the  more  variable  is  the  boiler  pressure. 

Theory. — This  can  be  most  clearly  apprehended  in  a  general 
way,  by  reference  to  an  analogous  device,  in  which  the  steam 


current  from  the  boiler  is  represented  by  a  visible  solid,  shot 
out  by  the  agency  of  an  elastic  medium.  See  Fig.  61,  where  A 
and  B  are  two  closed  air  vessels,  fixed  on  a  common  support  D, 
and  connected  by  a  tube  C  ;  and  thus  charged  alike  by  a  con- 
densing syringe  attached  to  either  of  them.  In  one  end  of  A, 
is  the  valve  e,  opening  inward ;  while  B  is  an  air  pistol,  dis- 
charging a  ball  through  a  tube,  T,  when  the  air  pressure  is  di- 
rected against  the  ball  by  the  springing  open  of  a  cock.  The 
ball  thus  discharged,  and  striking  the  valve  e,  will  open  it,  and 
enter  the  chamber  A. 

To  understand  this,  we  have  only  to  consider  the  difference 
between  stationary  pressure  and  the  accumulated  force,  repre- 
sented by  a  moving  mass. 

Pressure,  as  100  pounds  to  1  square  inch,  against  an  un- 
yielding resistance,  and  continually  neutralized  by  it,  is  a  unit, 
as  compared  with  the  living  force  developed  by  the  motion  of 
a  heavy  mass,  and  representing  the  sum  of  the  units  due  to  the 
repeated  action  of  this  pressure  in  producing  more  and  more 
motion  at  each  instant  while  the  pressure  acts. 

Thus,  the  force  exerted  by  the  ball  upon  the  valve  e,  repre- 
sents the  sum  of  all  the  effects  produced  upon  the  ball  by  the 
pressure,  in  all  the  instants  while  it  is  passing  through  T ;  while 


188  ELEMENTS   OF 

the  resistance  of  the  valve  e  is  due  to  the  equal  pressure  ex- 
erted on  it  in  only  the  single  instant  in  which  it  opens. 

Or,  in  other  words,  before  all  parts  concerned  can  come  to  rest, 
there  must  be  an  equation  of  works.  WorJc  is  the  product  of 
weight  into  space  passed  over ;  and  the  work  represented  by 
the  motion  of  the  ball,  must  be  given  out  before  the  ball  can 
stop.  But  without  motion  there  can  be  no  work ;  hence,  when 
the  ball  encounters  the  valve,  held  down  by  a  pressure,  less 
than  will  resist  the  whole  indenting  effect  of  the  ball  upon  an 
unyielding  mass,  motion  will  be  imparted  to  the  valve. 

Returning  now  to  the  injector,  the  valve  J,  unyielding  in  a 
direction  from  the  boiler,  receives  the  static  pressure  of  the 
water  from  the  boiler,  and  is  analogous  to  the  valve  e,  above. 
The  issuing  steam  is  analogous  to  the  ball  shot  from  T,  and  no 
less  so,  though  of  the  same  form  of  matter  as  the  agent  which 
propels  it,  viz.,  other  steam  in  the  boiler,  discharging  itself  by 
its  own  elastic  force.  This  discharged  steam,  reducing  its  ve- 
locity by  mixture,  in  condensation,  with  many  times  its  weight  of 
water,  will  still  force  open  the  valve  J,  so  long  as  the  quantity  of 
water  taken  along  with  it,  gives  a  velocity  and  living  force  to 
the  entering  jet  of  combined  steam  and  water,  greater  than  the 
living  force  of  a  jet  of  water  alone  issuing  from  the  boiler. 
And  this  is  just  what  really  occurs. 

A  point  of  difference  between  the  injector  and  the  air  pistol, 
and  in  favor  of  the  former,  is  that  the  dilatation  of  the  freely 
escaping  steam,  which  is  further  increased  by  the  tendency  to  a 
vacuum  constantly  existing  by  reason  of  condensation  at  its 
contact  with  the  water,  increases  its  velocity,  and  hence  its 
living  force.  The  living  force  of  a  unit  of  weight  of  steam  at 
its  issue,  represents  a  quantity  of  work,  measured  by  the  vieight 
of  that  steam,  falling  through  the  height  to  which  its  particles, 
considered  as  projected  atoms,  would  ascend  by  reason  of  their 
velocity  of  issue  from  the  steam  nozzle.  And,  as  before,  so 
long  as  the  additional  weight  of  water  drawn  into  the  steam  jet 
does  not  reduce  the  velocity,  and  consequently  the  living  force 
of  the  mingled  jet  to  less  than  that  of  water  alone  of  the 
same  temperature  issuing  directly  from  the  boiler,  the  former 
will  prevail  and  enter  the  boiler. 

If  the  steam  pressure  in  the  boiler  be  increased,  the  steam  jet 
will  have  a  greater  velocity,  but  still  more,  an  increased  weight 
relative  to  the  water  portion  of  the  jet,  comparing  units  of  each. 


MACHINE   CONSTRUCTION   AND   DRAWING.  189 

Hence  it  will  take  up  a  less  number  of  times  its  own  weight 
of  water  before  reducing  the  living  force  of  the  feed  jet  to  less 
than  that  of  a  water  jet  alone  from  the  boiler.  That  is,  the 
lower  the  boiler  pressure  the  more  effective  relatively  will  be  the 
injector.  Thus,  an  injector  which  will  deliver  200  cubic  feet 
of  water  per  hour  under  a  steam  pressure  of  50  Ibs.  per  square 
inch,  will  deliver  but  264  cubic  feet  at  100  Ibs.  per  square  inch, 
and  328  cubic  feet  at  150  Ibs.  per  square  inch. 

If,  however,  the  water  supplied  at  K  were  too  hot  to  permit 
the  condensation  of  the  steam,  the  injector  would  cease  to  act; 
and,  accordingly,  the  hotter  the  feed  water,  the  less  will  be 
thrown  into  the  boiler.  Combining  this  with  the  preceding  re- 
sult, greater  heat  of  feed  water  can  be  purchased  by  the  sacri- 
fice of  quantity  /  and  this  can  be  done  more  fully,  the  less  the 
steam  pressure.  Hence,  directions  for  using  the  injector  give 
the  maximum  advisable  temperature  for  different  boiler  pres- 
sures. Thus,  at  a  steam  pressure  of  30  Ibs.  per  square  inch,  the 
temperature  of  the  feed  water  may  be  130°  F. ;  at  100  Ibs. 
pressure,  the  feed  may  be  at  110°  F.,  etc. 

A  full  physico-mechanical  theory  of  the  injector,  treated  an^ 
alytically,  and  with  numerical  computations,  is  given  from  M. 
Combes  in  the  Journal  of  the  Franklin  Institute  for  May,  1860, 
and  an  extended  general  'explanation  and  description  of  its  sev- 
eral applications,  in  the  same  Journal  for  July,  August,  and 
September,  1868.  To  these,  from  which  the  foregoing  was 
partly  taken,  the  reader  is  referred  for  particulars  which  belong 
more  to  physical  mechanics  than  to  this  work. 

Construction. — PI.  XXIY.,  Fig.  5,  shows  a  section  through 
the  axis  of  the  injector,  which  is  here  supposed  to  be  horizontal, 
as  is  usual  in  practice.  As  nearly  every  section  perpendicular 
to  the  axis,  would  show  only  circles,  any  number  of  cross  sec- 
tions can  be  made  by  the  student. 

The  figure  was  prepared  from  a  beautiful  model  presented 
by  the  makers,  Win.  Sellers  &  Co..  and  differing  from  the  work- 
ing form  only  in  having  a  quarter  of  the  case  cut  out  so  that 
the  interior  was  exposed,  without  taking  the  instrument  to 
pieces. 

The  injector  is  made  of  various  sizes.  By  taking  the  diame- 
ter of  each  of  the  openings  A,  K,  and  L  as  1  inch,  it  will  serve  as 
a  scale  for  the  drawing,  in  the  present  example. 


190  ELEMENTS   OF 


CLASS  Y.-MODULATORS. 

124.  MODULATORS   (39)  serve  to    discontinue    motions  that 
would  otherwise  go  on ;  to  maintain  motions  that  would  other- 
wise stop  even  though  the  motive  power  were  not  withdrawn  ;  to 
change  the  relative  directions  of  motions  ;  or  the  ratio  of  their 
velocities  ;  and  that,  suddenly,  or  gradually. 

The  term,  modulators,  is  preferred  to  modifiers,  on  account  of 
its  less  common  use  and  consequent  greater  precision.  If  to 
modify  be  to  adapt  a  general  law  to  a  special  case,  then  to 
modulate  may  be  to  impress  a  determinate  law  of  change,  or  a 
change  according  to  a  determinate  law,  upon  a  given  form  of 
action. 

125.  Many,  if  not  most,  modulators  are,  like  many  regulators, 
compound  organs  or  sub-machines,  and  few,  if  any  simple  mod- 
ulators  afford  valuable    drawing    exercises,  after  what  have 
already  been  presented.     This  entire  class  of  organs  may  there- 
fore here  be  passed  over  with  a  few  remarks  upon  the  examples 
mentioned  in  the  column  of  modulators  in  the  Table  I. 

A — Point  Modulators. 

126.  An  idler  pulley  is  merely  a  small  wheel,  or  roller, 
mounted  in  a  swinging  frame,  or  in  movable  bearings  ;   so  that 
it  can  be  pressed  against  a  belt,  to  tighten  it,  and  give  it  a  firm- 
er hold  upon  a  pair  of  band  wheels,  or  to  throw  them  in  and 
out  of  gear  if  need  be. 

B — Line  Modulators. 

127.  An  escapement  is  a  purely  mechanical  means  for  con- 
verting an  oscillating  into  a  rotary  motion  in  one  direction  by 
alternately  engaging  and  disengaging  peculiarly  adjusted  arms, 
with  the  teeth  of  a  peculiarly  designed  wheel.     It  also  serves 
for  regularly  intermitting,  for  the  purpose  of  restraining,  a 
motion  that  might  otherwise  soon  run  down.     To  be  of  much 
use  or  interest  as  a  subject  of  study,  it  must  be  shown  in  connec- 
tion with  the  parts  adjacent  to  it,  and  is  therefore  deferred  till 
the  chapter  on  compound  organs  shall  be  read. 

128.  Sand  shifters  are  very  generally  moved  by  an  adj  ust- 


MACHINE   CONSTRUCTION   AND   DRAWING. 


191 


able  projecting  piece  called  a  dog,  which  is  clamped  to  some 
moving  part  of  a  machine,  as  the  table  of  an  iron  planer,  so  as 
to    operate   a  jointed    lever 
which    carries   the    shifting 
arm. 

129.     Clutches 


generally 

are  devices  for  coupling  or  r@ 
uncoupling  at  pleasure  the 
successive  pieces  in  a  line  of 
shafting,  or  of  causing  the 
shaft  to  communicate  its  mo- 
tion or  not. 

Fig.  62  represents   a  pin 

clutch,  in  which  the  disk  A,  is  keyed  to  the  shaft,  C,  by  the  long 
feather,  dd,  and  is  pierced  with  holes,  into  which  the  pins  of  the 
disk,  B,  enter.  Now  if  B  revolve  loosely  on  the  shaft,  or  if  it 
be  keyed  to  a  shaft,  which  is  divided,  between  the  disks,  the 
shaft  C,  with  A  and  B,  will  all  revolve  together  by  pressing  up 
A  against  B  till  the  pins  enter  the  holes  in  A. 

130.  /Simple  slide  rests  are  merely  stationary  supports,  ad- 
justable to  any  position  for  the  cutting  tool  held  by  the  operator 
of  a  hand  lathe. 


C— SURFACE  MODULATORS. 

a — Plane  Modulators. 


131.  Variable 
Fig.  63  shows  what  may  be 
called  a  plane  variable  crank. 
A  and  B  are  two  disks.  A 
contains  the  radial  slot,  j9^, 
and  B  the  spiral  slot,  indi- 
cated by  a  single  line,  pkq. 
If  now,  a  crank-pin, p,  be  free 
to  move  in  both  slots,  it  will 
follow  both,  and  give  a  va- 
riable angular  velocity  to  A, 
which  may  be  varied  by  re- 
volving B  in  the  same  way 
at  a  less  speed,  in  the  opposite  way,  or  not 


192 


ELEMENTS    OF 


b — Developable  Modulators. 

132.  Speed  pulleys  (Fig.  64)  are  familiar  objects 
in  all  machine  shops,  for  altering  the  speed  of  any 
given  machine  according  to  the  work  to  be  done 
upon  it,  by  shifting  the  band,  J,  from  one  to  an- 
other of  the  pulleys,  all  of  which  revolve  011  the 
Such  band  pulleys  are  arranged  in  two  sets  with 
the  largest  of  one  set  opposite  to,  and  working  with,  the  small- 
est of  the  other,  and  with  the  sum  of  the  diameters  of  any  pair 
that  act  together  constant. 

The  following  theorem  and  problem  express  the  main  points 
of  interest  relative  to  speed  pulleys. 


THEOREM  XXI. 

If  the  band  l>e  crossed,  it  will  l>e  equally  tight  on  every  pair 
of  opposite  pulleys. 

Let  BC  and  DE,  Fig.  65,  be  the  radii  of  a 
pair  of  pulleys ;  and  CE,  a  common  tangent, 
a  portion  of  the  crossed  band.  Make  BF 
parallel  to  CE,  and  hence  tangent  to  the  cir- 
cle DF  =  DE  +  CB. 

Now  since  similar  arcs  are  as  their  radii, 
and  measure  the  same  angle  at  the  centre, 
they  may  be  represented  by  that  angle,  mul- 
tiplied by  their  respective  radii.     Also  note 
that  ABO  =  FDG,  and  we  have 
HE  +  EC  +  CA  =  EC  +  DH  •  m  +  BC  •  in 
=  EC  +  DF  •  m 
=  BF  +  FG. 

That  is,  the  half  length,  and  hence  the  whole 
length,  of  the  band  is  constant  for  any  pair 
of  pulleys  whose  added  diameters  equals  DF.   Hence,  as  stated, 
the  band  will  be  of  uniform  tightness. 


MACHINE   CONSTRUCTION   AND   DRAWING. 


193 


PROBLEM  X. 

To  form  a  set  of  speed  pulleys  to  give  a  series  of  velocity 
ratios  in  geometrical  progression. 

Let  the  greatest  and  least  diameters  of  the  pulleys  be  6 
inches  and  15  inches.  As  both  sets  are  alike,  the  extremes  of 
the  series  of  velocity  ratios  will  be  reciprocals  of  each  other, 
viz. : 

1    and   1?   or  2    and   1 

15  652 

Now  let  there  be  three  intermediate  ratios ;  that  is,  terms  to 
this  series. 

The  property  of  a  logarithmic  spiral,  that  its  equidistant  radii 
are  in  geometrical  progression,  enables  us  to  find  the  required 
terms  graphically. 

To  construct  the  spiral,  make  a  figure  as  follows,  Fig.  66, 


AC  :  AB  :  :AE  :  AD  :  :  AG  :  AF,  etc.  ; 
AC  :  AE  :  :  AE  :  AG  :  :  AG  :  AI,  etc. 


where 
or 

Thus  AC,  AE,  AG,  etc.,  are  in  geometrical  progression.  Now 
describe  a  circle  with  any  convenient  radius  A£,  Fig.  67,  divide 
it  into  any  number  of  equal  parts,  tic,  etc.  The  smaller  these 
parts  and  the  larger  the  radius  A5,  the  more  accurate  will  be 
the  results  to  be  obtained. 

Then,  beginning  on  A5,  for  example,  make  Aa  =  Aa,  Fig. 

66  ;  AC  =  AC,  Fig.  66  ;  AG  =  AG,  Fig.  66,  etc.     To  avoid 

confusion,  not  all  the  radii  from  AC  to  Ao,  Fig.  67",  are  shown, 

on  which  the  successive  distances  from  AC  to  Aa}  Fig.  66,  are 

13 


194 


ELEMENTS   OF 


laid  off.     The  curve  through  a,  e,  C,  E  .  .  .  .  K  will  be  the  re. 
quired  auxiliary  spiral. 

Now,  in  the  given  example,  the  extreme  ratios  are  -fa  and  ^, 
or  -|  and  2£.  Then  take  these  distances  as  radii  on  any  con- 
venient scale  (a  scale  of  inches  was  used  in  this  construction), 
and  A  as  a  centre,  and  describe  arcs,  intersecting  the  spiral  at 
p  and  T.  Finally,  divide  PT,  where  P  is  on  Ap  produced, 


MACHINE   CONSTRUCTION   AND   DRAWING.  195 

into  four  equal  parts,  and  draw  the  radials  AQ,  AH,  etc., 
through  the  points  of  division,  and  A^,  A/1,  and  As  will  be  the 
three  desired  intermediate  terms  of  the  progression,  of  which 
Ap  =  |,  and  AT  =  2£,  are  the  extremes. 

These  distances  are  the  values  of  the  ratios  of  the  velocities 
of  the  successive  pairs  of  pulleys  of  the  required  set,  and  the 
sum  of  the  diameters  of  these  pairs  is  constant.  We  have  then 
to  divide  a  given  line  into  two  parts  having  a  given  ratio. 
How  shall  this  ratio  be  expressed  ?  Six  and  fifteen  are  the 
diameters  of  the  extreme  pulleys  which  act  together,  and  to 
express  their  ratio,  and  thus  that  of  their  velocities,  by  a  propor- 
tion, we  have 

15:6::!:^,  or  |, 

and  a  like  proportion  would  be  found  for  each  pair  of  opposite 
pulleys.  Hence  let  MIST,  Fig.  68,  represent  the  full  size  of  the 
constant  sum  of  the  diameters,  =  21  ins.  That  is,  in  the  actual 
case  supposed,  MN  would  be  21  ins.  We  shall  then,  as  shown 


N 


in  the  figure,  divide  it  first  into  two  parts  whose  ratio  shall  be  Aq, 
that  is  two  parts,  MX  and  NX,  which  shall  be  to  each  other  as 
1  and  A.qr,  1  being  1  unit  of  the  same  scale  (inches  in  Fig.  67), 
from  which  Ap  =  -|,  and  AT  =  f ,  were  taken.  The  parts  of 
MN  will  be  the  diameters  of  one  pair  of  pulleys.  Next  divide 
MIS'  into  two  parts,  which  shall  be  to  each  other  as  1  and  Ar, 
etc. 

By  constructing  all  these  figures  of  large  size  and  in  fine 
lines,  on  very  heavy  smooth  paper,  and  with  a  foot  instead  of 
an  inch  for  the  unit,  MA,  Fig.  68,  of  the  scale  on  which  Ap, 
Ar,  etc.,  Fig.  67,  are  laid  off,  the  results  will  doubtless  be  prac- 
tically as  accurate  as  if  found  by  computation. 

133.  Cone  pulleys,  Fig.  69,  are  another  device  for  adjusting 
velocity  ratio ;  but,  by  imperceptibly  small  variations  instead  of 
definitely  differing  ones,  as  in  the  use  of  speed  pulleys. 

134.  Dead  pulleys  revolve  loosely  on  their  shafts,  so  that  when 


196 


ELEMENTS   OF 


i  band  is  shifted  to  them  the  machine  driven  by  that  shaft 

jtops. 

135.  Sectoral  motions,  Fig. 

FIG.  69.  TO,   afford    variable   velocity 

ratios  by  toothed  sectors,  ar- 
ranged in  parallel  planes,  so 
that  any  two,  which  act  to- 
gether, are  in  the  same  plane 
and  the  sum  of  the  radii  is 
constant  and  equal  to  OQ,  the 
distance  between  the  parallel 
axes  of  motion. 

A  clearer  idea  of  such  mo- 
tions may  be  had  by  analyzing 
Fig.  70.  Let  the  revolution 
be  in  the  sense  of  the  arrows, 
and  let  the  equal  quadrants  M 
and  M7  begin  contact  at  A. 


FIG.  70. 


Then,  after  a  quarter  revolution,  a  and  a  will  be  together  at  A. 
Then  the  quadrant  N'  engages  with  N,  and  after  another  quarter 
revolution  of  Q,  5  and  b  will  unite  at  B.  Arc  db  =  dbonW  and 
the  velocity  ratio  is  as  Qd  to  Od.  Then  R,  and  R'  act  together, 


MACHINE   CONSTRUCTION   AND   DRAWING. 


197 


with  the  velocity  ratio  ---  till  c  and  c'  coincide  at  C.     O  has 

now  made  a  complete  revolution,  but  Q  has  made  less  than  one 
revolution  by  the  angle  c/QA,  gc  being  equal  to pfc.  To  bring 
the  radii  QA  and  OA  of  the  quadrants  M  and  M'  together 
again  at  A,  the  wheel  Q  alone  must  revolve  through  the  angle 
CQ</.  For  this,  an  imaginary  sector,  of  radius  QO,  must  act 
with  a  like  sector  of  radius  =  0  at  O.  Otherwise,  cut  off  R' 
by  the  radius  Q<?,  and  R,  by  the  arc  cf=  ec',  and  then 
divide  QO  into  segments  inversely  as  the  arcs  Am  and  An,  for 
the  radii  of  a  fourth  pair  of  sectors,  QA/H,  and  OAH,  marked 
S'  and  S,  which  will  cause  M  and  M'  to  begin  contact  again 
after  one  complete  and  simultaneous  revolution  of  each  wheel. 

136.  Elliptic  gears,  when  used  merely  to  make  a  motion 
quick  in  some  parts  and  slow  m  others,  and  not  arbitrarily,  but 
for  a  special  reason,  are  modulators.     They  are  simply  equal 
and  similar  toothed  elliptic  wheels,  with  teeth  formed  by  a  con- 
stant generating  circle  as  in  circular  gearing.    But  their  centres 
of  motion  are  foci,  at  a  distance  apart  equal  to  the  transverse 
axis,  and  the  point  of  contact  will  then  be  on  the  line  of  centres. 
Elliptic  gears  are  sometimes  seen  in  slotting  machines,  for  planing 
such  parts  as  the  insides  of  connecting  rod  straps,  where  the 
cutting  tool,  instead  of  the  piece  to  be  planed,  travels  back  and 
forth.     Hence,  it  is  a  valuable  saving  of  time  to  have  the  tool 
move  faster  on  its  back  stroke  when  it  is  idle  ;  as  the  planer 
table  does  when  it  travels  under  a  fixed  tool.     The  driving 
ellipse  revolves  uniformly,  then  its  longer  radii  will  act  with 
the  shorter  ones  of  the  follower,  giving  the  latter  a  high  angu- 
lar velocity,  during  the  retreat  of  the  tool,  and  contrariwise 
during  the  advance  of  the  tool. 

c — Warped  Modulators. 

137.  The  helicoidal  dutch,  Fig.  71,  is  merely  one  in  which 
the  coinciding  edges,  as  ab,  may 

be  helices,  and  boundaries  of 
right  helicoidal  surfaces.  They 
come  together  easily,  and  if  B 
be  the  driving  shaft  revolving 
as  shown  by  the  arrow,  it  has 
fair  bearing  surfaces,  as  ac,  at 
right  angles  to  the  direction  of  motion. 


198  ELEMENTS   OF 

d — Double  Curved  Modulators. 

138.  Double  curved  speed  pulleys,  Fig.  72,  may  have  various 
forms,  according  to  the  particular  condi- 
tions, not  necessary  to  discuss  here,  which 
may  be  imposed  upon  them.  Thus,  equal 
lateral  shifts  of  the  belt  may  be  required 
to  produce  equal  differences,  or  equal  ra- 
tios of  successive  velocity  ratio.  But  an 
analytical  discussion  of  such  data  is  a  use- 
less refinement,  since,  unless  the  band  be 
reduced  to  a  perfectly  inextensible  and  un- 
slipping  Ivne,  the  results  obtained  would  not  hold  in  practice. 


MACHINE  CONSTRUCTION  AND  DRAWING.  199 


CLASS  VL-OPERATORS. 

139.  Operators  (39)  are  those  parts  in  any  machine  which 
act  directly  on  the  raw  material,  or  to  accomplish  the  work  to 
be  done  ;  as  the  piston  or  plunger  in  a  pump  ;  the  cutter  in  a 
wood  or  iron  planer  ;  the  shuttle  in  a  loom,  etc.  They  are  really 
tools,  operated  by  a  machine  instead  of  by  hand ;  and  here  it 
may  be  noted  that  when  machines  are  used  in  making  other 
machines,  which  in  turn  are  employed  in  the  manufacture  or 
preparation  of  articles  generally  used,  such  as  clothes,  newspa- 
pers, etc.,  the  former  are  now  often  called  tools.  Thus  lathes, 
planers,  drills,  and  the.  other  machines  of  the  machine  shop,  are 
advertised  and  known  as  machinists'  tools,  while  hand  tools,  as 
wrenches,  files,  etc.,  are  often  called  bench  tools  (31). 

Though  few  of  the  examples  in  the  column  of  operators  in 
the  General  Table  need  illustration,  on  the  plates,  yet  several 
are  of  interest  to  mention  briefly. 


A — Point  Operators. 

140.  Movable  saw  teeth,  a  recent  invention,  may  here  be  men- 
tioned first,  by  reason  of  the  magnitude  of  the  lumber  manu- 
facture. 

Fig.  73  represents  a  tooth  for  sawing  small  logs.  Above  the 
line  AB  it  is  tempered  ;  the  rest  is  soft  enough  to  bend  without 
breaking.  This  allows  the  throat  A,  Fig.  74,  to  be  made  larger 
than  in  solid  saws,  where  the  whole  saw  is  tempered.  A  larger 
clearance  is  thus  afforded  for  the  shavings  and  dust  cut  away  by 
the  teeth.  The  perforations  allow  the  teeth  to  retain  their  form 
as  they  wear  out.  The  teeth  are  made  wider  at  the  point,  P,  so 
that  the  whole  surface  of  the  saw  will  not  press  against  the  log. 

Fig.  74  shows  a  fragment  of  a  saw,  showing  how  the  teeth  are 
inserted  in  the  plate. 

A  shows  a  tooth  inserted  in  a  section  or  piece  of  the  saw  plate 
E.  D  the  rivet,  one-half  in  the  saw  plate  and  one-half  in  the 
tooth.  B,  the  incision  in  the  saw  plate,  has  a  V  rib  made  on  the 


200 


ELEMENTS   OF 


plate  to  fit  the  corresponding  groove  in  the  tooth  C.  The  tooth 
is  inserted  in  the  following  manner:  Place  the  groove  in  the 
back  or  convex  part  of  the  tooth  on  the  Y  that  is  fitted  to  re- 
ceive it,  driving  the  end  which  has  one-half  of  the  rivet-hole  in 


FlO.  74. 


MACHINE    CONSTRUCTION   AND    DRAWING. 


201 


it  into  the  saw  plate  from  the  side,  then  put  in  the  rivet  and 
head  it  up  to  fill  the  countersink,  and  cut  or  file  it  off  smooth 
with  the  plate,  when  the  tooth  Mail  be  held  as  firmly  in  the  saw 
as  a  solid  tooth.  The  teeth  are  made  thicker  at  the  point  than 
the  saw  plate,  so  they  can  be  easily  spread  to  give  them  the  re- 
quired set,  and  new  teeth  can  be  inserted  in  case  an  old  one 
breaks  or  is  torn  out,  which  seldom  happens. 


Fig.  75  shows  an  arc  of  one  of  these  saws  in  operation,  and 
with  the  under  side  of  the  tooth,  AB,  tangent  to  a  circle,  CB, 
of  three-fourths  of  the  radius  of  the  saw,  the  latter  radius  being 
estimated  from  the  points  of  the  teeth. 

141.  Figs.  76  and  77  represent  a  recent  improvement  called 


PICK  76  represents  a  segment  of  a  cross-cutting  Circular  Saw,  10  inches  in  diameter. 


202 


ELEMENTS   OF 


perforated  saws.     They  are  said  to  possess  many  advantages, 
such  as  the  saving  of  frequent  "  gumming,"  that  is  cutting  or 


FIG.  77  represents  a  segment  of  a  Circular  Splitting  Saw,  16  inches  in  diameter. 


filing  out  the  throats  of  teeth  as  they  wear  away ;  prevention  of 

expansion  of  the  rim,  and  fracture  at  the  inner  angle  of  such  a 

pointed  throat  as  may  be  left 
by  filing.  Line  2,  Fig.  76, 
shows  the  line  of  wear,  and  3 
the  last  tooth  before  the  saw 
is  worn  out.  The  labor  of 
trimming  the  inner  edges  left 
by  breaking  out  the  bars  be- 
tween the  perforations  is  small. 
Fig.  78  represents  a  new 
patent  form  of  cross-cut  saws ; 
the  short  or  clearing  teeth  are 
about  -j^-  in.  shorter  than  the 
long  or  cutting  teeth,  and  act 
to  clear  the  kerf  of  saw  dust. 

142.  Fig.  79  shows  the  usual 
form  of  saw  teeth,  with  the 
pio  7g  teeth  bent  alternately  to  right 

and  left,  to    make   the   kerf 

wider  than  the  thickness  of  the  saw  plate. 
Movable-toothed  circular  saws  are  made  of  all  diameters 

from  8  to  88  inches,  and  solid  perforated  ones  from  4  to  72 

inches  diameter. 


MACHINE   CONSTRUCTION   AND   DRAWING.  203 

With  a  saw  properly  hung  in  a  true  vertical  plane,  and  firm 
on  its  axis,  or  mandrel,  and  with  the  log  carriage  running  steadi- 
ly true  on  a  firm  bed,  9,000  feet  per  minute  is  pronounced  a 
proper  speed  for  the  rim  of  a  circular  saw. 


EXAMPLE  L. 
LyaWs  Positive  Motion  Shuttle. 

Description. — By  a  "positive  motion  "  is  meant  one  in  which 
the  moving  piece  is  taken  hold  of  by  that  which  moves  it,  so 
that  it  must  move  unless  there  be  an  obstruction,  sufficient  to 
break  the  connection  between  the  pieces.  This  is  the  character 
of  most  mechanical  movements.  On  the  other  hand,  the  motion 
of  a  fly-wheel  after  all  steam  has  been  shut  off,  that  of  a  valve 
closed  by  a  weight,  or  the  natural  flow  of  water  through  an  open 
pipe,  are  passive  motions.  In  other  words,  positive  or  necessary 
motions  take  place  because  they  must,  while  passive  or  free 
motions  continue  because  nothing  actively  prevents. 

Now  the  motion  of  the  shuttle  of  a  loom  is  of  the  latter  class. 
Any  one  who  has  seen  the  operation  of  either  hand  or  power 
weaving,  will  remember  that  the  shuttle  is  thrown  through  be- 
tween the  wrarp  threads  by  hand,  or  by  a  rod  called  a  picker  staff, 
whose  upper  or  free  end  gives  the  shuttle  a  quick  thrust,  and 
then  leaves  it  to  find  its  way  across  the  loom. 

[The  remainder  of  this  description  is  condensed  from  the 
"  Scientific  American,"  and  the  "  American  Artisan."] 

Notwithstanding  the  persistence  with  which  these  methods 
of  actuating  the  shuttle  have  continued,  there  have  always  ex- 
isted serious  difficulties,  which  it  was  desirable  to  obviate, 


204:  ELEMENTS    OF 

Without  entering  too  minutely  into  details,  we  will  specify  a  few 
important  defects,  that  the  important  advantages  which  the 
device  under  consideration  is  destined  to  accomplish  may  be 
understood. 

First,  the  distance  to  which  the  shuttle  can  be  thrown  with 
certainty,  either  by  the  hand,  or  by  the  use  of  the  picker  staff, 
is  limited;  and  the  difficulty  of  weaving  wide  goods  is  con- 
sequently greater  than  that  of  making  medium  or  narrow  tex- 
tures of  the  same  kind. 

Second,  the  motion  of  the  shuttle,  having  no  positive  relation 
to  the  other  parts  of  the  loom,  the  operator  has  no  control  over 
it  during  the  time  it  is  traversing  the  distance  between  the 
shuttle  boxes ;  and  the  motions  of  the  other  parts,  if  by 
accident  they  should  take  place  a  little  too  soon  from  any  cause, 
are  liable  to  clash  with  that  of  the  shuttle.  To  illustrate  this, 
suppose  the  shuttle,  impelled  by  too  feeble  a  stroke,  to  pause 
in  its  passage.  In  a  power  loom  of  the  ordinary  construction 
the  lay,  or  vibrating  frame  which  drives  home  the  transverse 
thread  to  its  place,  would  then  make  its  beat,  and  either  drive 
the  shuttle  through  the  warps,  making  an  extensive  breakage, 
or  would  spring  the  dents  of  the  reed,  or  it  would  do  both. 

In  weaving  fine  goods,  the  bending  of  the  dents  cannot  be 
wholly  repaired.  They  cannot  be  again  perfectly  straightened 
without  taking  the  piece  out  of  the  loom,  and  if  the  piece  is 
woven  to  the  end  with  such  a  defect  in  the  reed,  a  slack  woven 
streak  will  appear  through  the  entire  remainder  of  the  tissue. 
In  order  that  the  shuttle  may  traverse  with  certainty,  a  regular 
speed  must  also  be  maintained,  below  which  it  is  impossible  to 
work  a  power  loom  with  success. 

Third,  the  shuttle  reaches  the  shuttle  box  after  its  flight  in 
either  direction,  and  comes  to  rest  before  the  lay  makes  its 
beat.  An  adjustment  so  perfect  that,  at  this  point,  the  threads 
of  the  weft  shall  be  firmly  drawn  up  against  the  exterior  threads 
of  the  warp  opposite  the  shuttle,  is  neccessary  to  make  a  perfect 
selvedge.  This  perfect  adjustment  is  difficult  of  attainment, 
so  much  so  that  the  character  of  the  selvedge  on  a  piece  of  linen 
or  silk  goods  is  one  of  the  criterions  by  which  the  quality  of 
the  fabric  is  determined. 

To  remedy  these  defects  entirely,  a  motion  radically  different 
was  required.  The  problem  may  be  enunciated  as  follows  : — 

Required   to  produce  a  positive  and  uniform  motion  in  a 


MACHINE    CONSTRUCTION    AND    DRAWING. 


205 


shuttle,  by  means  of  an  external  appliance  moving  exteriorly  to 
the  sheds  of  the  warp  without  positive  connection  between  the 
shuttle  and  the  motor  through  which  it  receives  its  motion.  A 


problem,  which  the  majority  of  mechanics  would  have  pro- 
nounced impossible,  had  not  its  possibility  been  demonstrated 
by  this  invention.  But  the  problem  is  further  complicated  by 


Fio.  81. 


ELEMENTS   OF 


another  condition  which  is  omitted  in  the  general  enunciation; 
namely,  no  lateral  motion  must  be  imparted  to  the  threads  of 
the  warp. 

The  ingenious  method  by  which  these  conditions  are  fulfilled 
is  shown  by  the  aid  of  the  accompanying  figures,  in  which 
Fig.  80  represents  the  loom  complete ;  Fig.  81  represents  all  the 
mechanism  of  the  positive  shuttle  motion — the  parts  not  neces- 
sary to  illustrate  this  being  omitted  ;  Fig.  82  is  a  front  view  of 
the  shuttle. and  its  driver;  Fig.  83  represents,  in  transverse 


section,  the  lay-reed  and  raceway  with  the  shuttle  and  its  car- 
riage ;  and  Fig.  84  is  a  diagram  illustrating  the  action  of  the 
shuttle-carriage  and  shuttle  upon  and  in  the  warp.  In  Figs.  82 


MACHINE   CONSTRUCTION   AND   DRAWING. 


207 


and  83  it  will  be  seen  that  the  shuttle  p,  is  furnished  with  two 
rollers,  4,  which  are  supported — the  lower  part,  ab,  of  the  shed 
of  the  warp  intervening  while  the  shuttle  passes  through  the 
shed — upon  two  rollers,  3,  in  the  carriage.  The  carriage  has 
two  lower  rollers,  2,  which  run  upon  the  bottom  of  the  lower 
rail  of  the  race-way,  £,  and  the  shuttle  has  two  upper  rollers,  5, 


which  run  against  the  bevelled  under  side  of  the  upper  rail,  w, 
of  the  race-way,  which  keeps  the  shuttle  in  place  in  front  of  the 
reed,  n. 

The  lay  is  carried  by  the  swords,  &,  in  the  usual  manner,  and 
the  movement  may  be  produced  either  by  a  crank-motion  or  by 
a  cam;  but  the  inventor  perfers  the  cam,  as  it  enables  the 
movements  of  the  lay  and  shuttle  to  be  better  timed.  The 
shuttle  carriage  is  connected  at  each  end  with  a  band,  u, 
Fig.  81,  which  passes  over  rollers  b,  at  each  end  of  the  lay ; 
thence  downward  and  under  two  rollers,  c,  attached  to  the 
lower  parts  of  the  swords,  and  around  a  horizontal  pulley,  d, 
near  the  floor.  Attached  to  this  horizontal  pulley,  there  is  a 
pinion  which  gears  with  a  horizontal  sliding-rack,  e,  which 
receives  a  reciprocating  motion  through  a  pitman,  f,  from  a 
crank- wrist,  g,  carried  by  a  disk,  A,  on  the  lower  end  of  a  ver- 
tical shaft  working  in  a  stationary  box,  a,  attached  to  the  out- 
side of  the  loom  framing.  On  the  upper  end  of  the  vertical 
shaft  there  is  a  bevel-gear,  i,  gearing  with  and  deriving  motion 
from  a  bevel-gear,^',  on  one  end  of  the  shaft,  A,  which  carries 
the  cams  for  operating  the  lay  and  those  for  producing  the  har- 
ness motion,  by  which  alternate  warp  threads,  as  ab  and  cb, 
Fig.  83,  are  alternately  raised  and  depressed,  so  as  to  interlace 
with  the  cross-thread  or  woof.  The  reciprocating  motion  given 
to  the  rack,  <?,  by  the  bevel-gears,^',  i,  vertical  shaft  crank-wrist, 


208  ELEMENTS   OF 

g,  and  pitman,  /,  produces,  by  its  action  on  the  pinion,  an  alter- 
nate or  reciprocating  rotary  motion  of  the  pulley,  d,  which  by 
alternately  winding  and  unwinding  the  band,  u,  on  opposite 
sides,  causes  the  band  to  move  the  shuttle  carriage  back  and  forth 
along  the  lay  and  under  the  warp,  thereby  causing  the  carriage 
to  carry  the  shuttle  back  and  forth  through  the  open  shed  of 
the  warp. 

One  important  feature  of  the  motion  is  that  the  carriage 
carries  the  shuttle  over  the  intervening  lower  shed  of  the  warp 
without  the  friction  which  «is  produced  by  the  fly-shuttle  and 
which  tends  to  break  the  warp.  The  manner  in  which  this  is 
effected  is  illustrated  by  the  diagram,  Fig.  84.  The  carriage  has 
not  even  the  slightest  tendency  to  produce  any  lateral  displace- 
ment of  the  warp  yarns.  The  lower  rollers,  2,  of  the  carnage  are 
caused  to  derive  a  rotary  motion,  like  that  of  the  wheels  of  a 
road  carriage,  in  their  passage  along  the  bottom  of  the  race- 
way, and  this  motion  is  imparted,  by  contact,  to  the  upper 
rollers,  3,  in  the  opposite  direction,  as  indicated  by  the  arrows 
on  the  rollers  in  Fig.  84,  since  rollers  2  are  in  slotted  bearings, 
so  that  the  weight  of  O  is  borne  by  rollers  3.  The  shuttle  is 
supposed  in  this  figure  to  be  moving  to  the  right.  The  dots,  6, 
represent  one  of  the  threads  of  the  warp  yarn  in  two  positions. 
The  roller,  3,  of  the  carrier  first  strikes  the  yarn  in  the  lower 
position ;  and  as  it  moves  along  with  the  carriage,  the  latter 
moving  to  the  right,  the  upper  part  of  the  roller,  3,  in  contact 
with  the  yarn  moves  just  as  fast  to  the  left,  and  so  does  not  tend 
to  carry  the  warp  with  it,  but  merely  lifts  up  the  latter  to  the 
higher  position.  The  rotary  motion  of  the  rollers,  3,  is  trans- 
mitted through  the  warp  to  the  lower  rollers,  4,  of  the  shuttle 
as  the  threads  of  the  warp  are  successively  passed  between  the 
rollers  3  and  4,  with  a  scarcely  perceptible  rolling  but  no  rub- 
bing motion. 

In  the  above-described  operation,  the  shuttle  being  acted 
upon  and  controlled  by  a  direct  and  continuous  connection  with 
the  motive  power,  its  action  is  absolutely  positive,  and  is  pro- 
duced with  very  little  power,  and  without  any  sudden  jerk. 
The  crank-wrist,  g,  is  so  arranged  as  to  gradually  overcome  the 
inertia  of  the  shuttle  at  starting  from  one  side  or  the  other  of  the 
loom,  producing  an  accelerated  motion  as  far  as  flie  centre  of  the 
lay,  and  afterwards  a  gradually  slower  movement — gradually 
checking  the  momentum  of  the  shuttle  as  it  approaches  the  other 


MACHINE   CONSTRUCTION   AND   DRAWING.  209 

side.  One  great  advantage  derived  from  this  is  that  the  weft 
is  not  subject  to  sudden  pulls  in  starting,  and  another  is  that 
the  shuttle  does  not  rebound,  and  a  tight  and  even  selvedge  is 
sure  to  be  produced.  Another  advantage  of  the  positive 
shuttle-motion  is  that  it  enables  goods  of  any  width  to  be 
woven.  It  is  as  easy  for  this  motion  to  carry  the  shuttle  through 
the  widest  as  through  the  narrowest  warp,  and  so  it  enables  the 
widest  goods  to  be  produced  at  the  same  cost  per  square  yard 
as  the  narrowest. 

Construction. — These  shuttles  are  of  various  sizes.  The  one 
shown  in  Figs.  82  and  83  is  on  a  scale  of  3  inches  to  1  foot. 
These  figures  may  therefore  be  drawn  to  scale  by  the  student. 


B — Line  Operators. 

143.  Among  linear  operators  may  be  placed  all  cutting 
edges,  whether  straight  or  curved.  Among  the  latter  are  the 
helical  edges  of  hay  cutters,  where  the  cutting  action  is  in  a 
radial  direction,  and  those  of  the  Ruggle's  slate  trimming 
machine  where  the  cutting  of  a  revolving  helical  edge  takes 
place  tangentially  to  the  imaginary  cylinder  on  which  the  edge 
is  traced. 

C— SURFACE   OPERATORS, 
a — Plane  Operators. 

EXAMPLE  LI. 
Air  Pump  Bucket  of  a  Marine  Engine. 

Description. — PI.  XXYIL,  Fig.  1.  represents  a  vertical  section 
of  the  bucket,  on  a  scale  of  1£  inches  to  1  foot.  As  the  bucket 
descends  in  the  air  pump,  the  water  of  condensation  below, 
from  the  well  K— A'K',  PI.  VIII.,  Fig.  1,  of  the  bed  plate, 
lifts  the  rubber  valve  through  the  gridiron  bottom,  and  fills  the 
bucket  above  the  valve.  Then,  as  the  bucket  rises,  being  open 
above,  the  water  in  it  and  the  external  air  close  the  valve  and 
the  water  is  emptied  into  the  hot  well  over  the  pump,  by  lift- 
ing the  floating  cover  of  the  air  pump,  which  is  tightly  held 
down  by  the  external  air  during  the  descending  stroke. 


210  ELEMENTS    OF 

This  pump  thus  removes  water,  as  well  as  air,  from  the  con- 
denser, but  on  the  latter  account,  which  is  the  most  important 
one,  it  is  called  an  air  pump. 

Construction. — All  the  principal  parts  being  circular  in 
plan,  a  half  plan  may  be  added  by  the  student  .with  sufficient 
accuracy,  and  the  scale  may  be  further  reduced  to  one-twelfth 
or  one-sixteenth. 

b — Developable  Operators. 

These,  in  the  form  mainly  of  cylindrical  or  conical  bending 
or  shaping  rolls,  as  used  by  sheet  and  plate  metal  workers,  or 
in  rolling  mills,  do  not  need  detailed  illustration. 

c— Warped  Operators. 
THE  SCREW  PROPELLER. 

Preliminary  Remarks. 

143.  Here  we  have  probably  the  most  important  example  of 
operators,  in  respect  to  the  magnitude,  and  the  scientific,  com- 
mercial, and  social  interest  of  its  applications. 

The  adequate  treatment  of  it,  alone,  would  be  enough  for  a 
volume,  and  must  detain  us  longer  than  that  of  any  other  ex- 
ample, though  only  the  elements  of  its  formation  and  action, 
treated  geometrically,  can  here  be  given. 

144.  Steam  vessels  have  for  a  long  time  been  propelled  by 
the  reaction  of  water  against  the  radial  floats  of  wheels,  one  on 
each  side,  and  usually  revolving  on  the  same  shaft ;  placed 
transversely  across  the  vessel.     Only  a  small  arc  of  the  cir- 
cumference is  submerged  at  once,  and  to  a  small  depth.     Such 
wheels  are  called  paddle  wheels. 

But,  of  late  years,  wheels  with  arms  or  blades  oblique  to  the 
wheel  axis,  placed  at  the  stern  of  the  vessel,  entirely  sub- 
merged, and  revolving  in  a  plane  perpendicular  to  the  path  of 
the  vessel,  have  been  increasingly  employed.  These  are  screw 
propellers.  They,  and  the  hulls  propelled  by  them,  have  been 
already  so  far  perfected  in  respect  to  mutual  adaptation,  that 
the  days  of  paddle  wheels  have  been  considered  as  numbered, 
except  for  use  in  waters  so  shallow  that  submerged  propellers 
would  be  inadmissible. 


MACHINE    CONSTRUCTION   AND    DRAWING.  211 

145.  The  screw  propeller  acts  upon  the  water  in  which  it  is  sub- 
merged, so  that  the  reaction  of  the  water  shall  impel  the  vessel 
to  which  the  propeller  is  attached,  in  the  direction  of  its  keel. 
The  vessel  is  supposed  to  be  free  to  move  under  the  action  of 
any  force  which  is  sufficient  to  overcome  the  relatively  small 
resistance  of  the  water,  by  friction  and  inertia,  to  cleavage  by 
the  passage  of  the  vessel  through  it.     Finally,  as  the  water  in 
which  the  screw  acts  is  confined  by  the  all  surrounding  water, 
its  reaction  becomes  effective  as  an  impelling  force.     So  much, 
only,  at  present,  for  the  general  idea  of  a  propeller. 

146.  The  study  of  the  screw  propeller  is  encompassed  with 
much  needless  obscurity,  arising  from  want   of    due   express 
recognition  of  the  few  simple  geometrical  facts  and  relations 
which  belong  to  it,  or  are  connected  with  it. 

The  treatment  of  it  will  therefore  next  be  cleared ;  first,  to  those 
who  have  not  kept  themselves  familiar  with  descriptive  geometry, 
by  a  brief  rehearsal  of  the  great  divisions  of  surface  and  lines, 
and  a  reference  of  the  propeller  surface  to  its  proper  geometrical 
position  ;  and,  second,  to  theoretical  students  by  a  popular  de- 
scription of  it,  and  precise  definitions  of  its  several  parts. 

Introductory  geometrical  Principles. 

147.  The  forming  of  a  line,  or  a  surface,  by  the  movement  of 
something  simpler,  is  called  its  generation.     The  moving  mag- 
nitude is  called  the  generatrix  /  any  fixed  point,  or  line,  which 
guides  this  motion  is  a  directrix  •  and  a  similarly  fixed  surface, 
is  called  a  director. 

Now,  any  line,  or  surface,  may  be  defined  in  two  ways,  first 
by  a  description  of  it,  consisting  of  the  enunciation  of  any  one 
or  more  geometrical  properties  possessed  by  it ;  or,  second,  by  the 
method  of  generating  it.  We  will  here  define  lines  and  sur- 
faces in  both  ways. 

148.  Any  line  is  generated  by  the  motion  of  a  point.     It 
consists  of  a  series  of  points  having  but  one  direction  at  any 
one  of  its  points,  and  but  one  dimension.     Every  surface  \s> 
generated  by  the  motion  of  some  line  of  constant  or  variable 
form.     It  has  extension  in  but  two  directions  at  any  one  oi?  its 
[>'/ints.     The  different  positions  of  the  generatrix  are  elements 
of  the  line  or  surface.     If  straight  lines,  they  are  called  straight 
or  rectilinear  elements.     If  two  elements  have  none  between 
them,  they  are  consecutive. 


212  ELEMENTS    OF 

149.  All  lines  are 

STRAIGHT,  or 
CURVED. 

A  straight  line  is  one  which  has  bnt  one  direction.  It  is 
generated  by  a  point  which  moves  without  change  of  direction 
towards  a  fixed  point,  the  directrix. 

A  curve  changes  its  direction  continually. 

150.  All  CURVES  are  either 

those  of  two  dimensions  =  plane  curves,  or 

"      "  three         "          =  curves  of  double  curvature. 

Plane  curves  are  also  called  curves  of  single  curvature,  and 

may  well  be  called  curves  of  two  dimensions.     They  are  such 

that  all  the  points  of  each  lie  in  the  same  plane ;  as  circles, 

ellipses,  cycloids,  letter  S,  and  figure  8  curves,  etc. 

151.  Curves  of  double  curvature,  may  well  be  called  curves 
of  three  dimensions  /  to  distinguish  them,  first,  from  compound 
curves,  like  polycentral  arch  curves ;  or  reverse  curves,  like  the 
letter  S,  which  are  naturally  enough  said  to  be  of  double  cur- 
vature ;  also,  second,  from  doubU  curved  surfaces,  with  which 
they  are  also  confounded  from  similarity  of  name.     The  points 
of  a  curve  of  double  curvature  cannot  all  lie  in  the  same  plane, 
as  in  case  of  the  handrail  to  circular  stairs,  for  example. 

The  Helix. 

152.  The  only  curve  of  double  curvature,  which  it  concerns 
us  here  to  mention,  is  the  Helix,  which  we  will  now  describe. 

If  a  point  simply  revolves  about  a  fixed  axis,  it  will  generate 
a  circle  perpendicular  to  that  axis.  If  it  moves  only  parallel 
to  that  axis,  it  will  generate  a  straight  line  parallel  to  the  axis. 
Combining  both  motions,  the  point,  by  both  revolving  and 
ascending — supposing  the  axis  to  be  vertical — will  describe 
some  form  of  helix.  Further,  if  both  motions  be  uniform,  the 
curve  will  be  the  common  helix. 

153.  The  ascension  of  the  helix,  while  making  one  revolution 
about  the  axis,  is  its  pitch. 

The  amount  of  pitch  for  one  revolution,  may  thus  be  the 
same  for  all  different  radial  distances  of  the  generatrix  from 
the  axis  in  different  helices.  But  in  this  case,  the  less  the  radius 
the  steeper,  evidently,  will  be  the  pitch,  as  circular  stairs  are 
steeper  at  their  central  part  than  at  their  circumference.  The 
pitch  may  be  as  great,  or  as  small,  as  we  please  to  make  it,  for 


MACHINE   CONSTRUCTION   AND   DRAWING.  213 

one  revolution.     If  great,  it  is  termed  coarse.     If  small,  it  is 
called  fine. 

The  more  general  forms  of  helix  may  have  a  variable  radius, 
as  well  as  pitch.  Such  would  lie  on  conical,  spherical,  or  other 
surfaces,  while  the  common  helix  evidently  lies  on  the  surface 
of  a  cylinder,  having  the  same  axis  as  the  helix. 

154.  All  SURFACES  are  either 

RULED,  or 
DOUBLE  CURVED. 

A  ruled  surface  is  any  one  on  which  a  straight  line  can  he 
drawn  in  one  or  more  directions.  It  is  generated  by  the  move- 
ment of  a  straight  line. 

A  double  curved  surface,  is  one  on  which  no  straight  line  can 
be  drawn,  as  a  sphere,  or  an  egg.  It  can,  therefore,  be  generated 
only  by  some  curve. 

155.  All  ruled  surfaces  are  either  plane,  or 

single  curved. 

A^plane  surface  is  one  on  which  a  straight  line  can  be  drawn 
in  any  direction.  It  is  generated 
by  a  straight  line,  moving  par- 
allel to  itself  upon  another  straight 
line;  by  a  straight  line  moving  in 
any  manner  upon  any  two  parallel  or 
intersecting  straight  lines ;  or  by  the 
revolution  of  a  straight  line  AB, 
about  another,  AC,  perpendicular  to 
it. 

.  156.  A  single  curved  surface,  is 
such  that  through  any  point  on  it,  at 
least  one  straight  line  can  be  drawn  ; 
as  on  a  cylinder,  or  cone.  It  is,  there- 
fore, generated  by  a  straight  line ;  moving  so  that  its  points  gene- 
rally, describe  curves. 

157.  All  single  curved  surfaces  are  either 

developable,  or 


A  developable  surface  is  one  which,  like  a  cylinder,  or  cone, 
can  be  rolled  out  upon  a  plane,  so  that  at  each  moment  it  will 
have  a  line,  or  element  of  contact  with  the  plane.  Such  a  sur- 
face is,  therefore,  generated  by  a  line  whose  consecutive  positions 


214 


are  parallel,  as  in  a  cylinder,  or  intersect,  as  in  a  cone.     That 
is,  they  are  in  the  same  plane. 

158.  A  warped  surface  is  one  which  can  have  no  element 
of  contact  with  a  plane,  which,  therefore,  cannot  be  made  to  lie 
in  a  plane  except  by  rending  its  consecutive  elements  from  their 
proper  relative  positions.     It  is,  therefore,  generated  by  moving 
a  straight  line  so  that  its  consecutive  positions  shall  not  be  in 
the  same  plane. 

159.  The  plastering  under  circular  stairs ;  the  working  sur- 
faces of  either  square  or  triangular  screw  threads,  and  of  pro- 
peller blades,   are  warped.     So  are  those  of  locomotive  cow 
catchers,   railway  snow  ploughs,  Jonval  turbine  water  wheel 
buckets ;  and  the  surface,  very  easily  illustrated  by  every  one 

for  himself,  formed  by  revolving  an  ob- 
lique line,  AB,  Fig.  86,  about  a  vertical 
axis,  T>d,  not  in  the  same  plane  with  AB. 

This  surface  is  called  a  kyperboloid  of 
two  united  nappes,  because,  by  examina- 
tion, any  section  of  it,  as  EF,  made  by  a 
plane  containing  its  axis,  is  found  to  be  a 
hyperbola  ;  of  which  T)d  is  the  conjugate 
axis.      Dd  being   vertical,  all  horizontal 
sections  of  the  surface  would  be  circles. 
The  least  one,  abc,  of  these,  is  called  the 
gorge.     If  its  radius  bd  became  zero,  the 
hyperboloid  would  become  a  cone  of  two 
equal  nappes,  of  which  d  would  be  the  common  vertex.     In 
geometry  these  two  nappes  are  considered  as  making  but  one 
complete  cone. 

160.  In  the  cow  catcher,  Fig.  87,  the  horizontal  bars  AC, 
ab,  etc.,  are  elements,  the  vertical  bar  AB,  over  the  rail,  and  the 

oblique  bar  CD,   over  the 
centre  of  the  track  are  direc- 
trices, and  AC,  etc.,  being  all 
parallel  to  the  ground,  the 
latter  is   the  director ,    in 
this  case,  a  plane  director. 
This  surface  is  called  a  hy- 
perbolic paraboloid,  because  all  its  curved  sections  are  parabo- 
las or  hyperbolas. 

161.  All  the  elements  of  the  hyperboloid,  Fig.  86,  make  the 


MACHINE   CONSTRUCTION    AND  DRAWING. 


215 


same  angle  with  any  plane  perpendicular  to  its  axis  T)d. 
Hence  such  a  plane  is  a  director,  this  simple  uniform  relation 
being  of  use  in  constructing  the  surface.  Hence,  also,  the  sur- 
face has  two  sets  of  elements,  as  AB,  and  mn,  inclined  equally, 
but  in  opposite  directions,  to  the  director. 

Likewise,  in  Fig.  87,  AC  and  BD  could  have  been  taken  as 
directrices,  and  AB  as  the  generatrix,  moving  upon  AC  and 
BD,  and  keeping  parallel  to  the  vertical  plane  ABE.  None 
but  these  two  warped  surfaces  have  this  property  of  having  two 
sets  of  elements.  We  have  dwelt  upon  them,  on  account  of 
their  simplicity,  in  order  to  lead  the  mind  to  a  conception  of 
warped  surfaces  generally. 

162.  Proceeding,  now,  to  the  screw  surf  ace.  If  an  indefinite 
line,  AB,  Fig.  88,  revolve,  horizontally,  that  is,  with  no  ascension, 


about  the  vertical  AC,  it  will  generate  a  horizontal  plane. 

If  it  only  move  upward,  parallel  to  itself,  it  will  generate  a 
vertical  plane. 

But  if  it  combine  both  motions,  loth  being  also  uniform,  it 
will  generate  "  a  spiral  surface,"  "  a  twisted  plane,"  geometri- 
cally termed  a  right  helicoid,  or,  more  specifically,  the  common 
right  helicone.  It  is  called  a  helicoid  because  the  path  of  any 
point,  as  B,  of  the  generatrix,  is  a  helix  BD  (152).  It  is  called  a 
right  helicoid  because  all  the  elements  AB,  «1,  etc.,  are  perpen- 
dicular to  the  axis  AC.  This  is  the  surface  of  the  under  side 
of  circular  stairs;  and  the  edges  of  their  steps  are  detached 
elements  of  a  similar  surface.  It  is  also  the  working  surface  of 
square  threaded  screw,  and  of  the  common  screw  propeller. 


216 


ELEMENTS    OF 


163.  The  height  on  AC,  attained  in  one  complete  revolution 
of  AB,  is  the  pitch  of  the  helicoid,  or  screw.  The  pitch  is  the 
same  for  all  points  of  AB,  since  all  ascend  equally  as  stated 
above.  But  the  circular  part  of  the  combined  motions  of  each 
point  is  greater  and  greater  as  its  radial  distance  from  the  axis 
AC  increases  ;  so  that  the  "  steepness  "  of  the  helicoid  is  greatest 
at  the  axis,  where  it  is  vertical,  and  is  less  and  less  the  further 
we  recede  from  the  axis  ;  just  as  circular  stairs  are  steepest  near 
the  central  post  about  which  they  wind,  and  flattest  at  their 
outer  circumference,  as  already  explained  in  describing  a  helix 
(152). 

164  Merely  for  completeness,  we  add,  Fig.  89,  that  if  we 
substitute  for  BA  (162)  a  line,  as  BD  or  BE,  to  revolve  uni- 
formly around  the  axis  AC,  while  it  also 
moves  uniformly  upward,  it  will  generate  an 
oblique  helicoid,  which  is  the  surface  of  a 
triangular  threaded  screw  thread.  Thus  if 
FG  revolve  about  AC,  the  two  being  parallel, 
it  will  generate  a  cylinder,  and  the  portion 
B<#0,  by  both  revolving  and  ascending  uni- 
formly, will  generate  the  thread  wound  upon 
that  cylinder.  The  common  helicoids,  both 
right  and  oblique,  thus  have  uniform  pitch. 

165.  Keturning  to  Fig.  88,  the  axis  AC,     A 

and  the  helix  described  by  any  point  of  AB,  FlG-  89- 

are  the  two  directrices  of  the  right  helicoid,  and  as  all  the  ele- 
ments are  perpendicular  to  AC,  they  will  all  be  parallel  to  a 
plane  which  is  perpendicular  to  AC. 

Such  a  plane  is,  then,  the  plane  director  of  the  helicoid. 
When  AC  is  vertical,  this  plane  will  be  horizontal. 

If  the  generatrix  ascend  faster  and  faster,  while  it  revolves 
uniformly,  the  helicoid  will  have  an  "  expanding  pitch."  Such 
a  helicoid  is  one  in  a  more  general  sense  than  one  having  a  uni- 
form pitch. 

166.  From  the  foregoing  geometrical  definitions,  we  will  pro- 
ceed according  to  (146),  with  a  more  practical  description  of  the 
screw  propeller,  as  actually  used. 

A  screw  propeller  is  essentially  the  same  in  form  and  action 
as  any  other  screw.  See  PL  XXIII.  It  differs,  first,  in  having 
a  much  greater  pitch  in  proportion  to  its  diameter ;  second,  in 
being  much  shorter,  so  that  each  of  its  threads,  called  arms  or 


MACHINE   CONSTRUCTION   AND   DRAWING.  217 

blades,  is  but  a  small  part  of  one  complete  convolution  of  a 
thread  about  the  axis,  and  third,  in  having  but  one  helicoidal 
face  to  its  blades,  whereas  the  threads  of  a  common  screw  are 
alike  on  both  sides,  to  enable  them  to  work  in  solid  nuts. 

167.  When  a  screw,  working  in  a  stationary  nut,  acts  upon 
any  movable  object,  both  advance,  and  that  equally.  In  screw 
propulsion,  water,  being  a  yielding  medium,  effectually  takes 
the  place  of  the  nut  only  to  certain  extent,  by  virtue  of  its 
weight,  incompressibilty,  and  inertia.  So  that  a  screw  propel- 
ler, revolving  in  water,  actuates  a  vessel  in  the  same  manner, 
though  not  to  the  same  extent,  as  a  common  screw,  working  in 
a  fixed  nut,  moves  an  object  placed  before  it. 


Slip. 

168.  The  difference  of  advance  in  the  two  cases  (167)  is  the 
slip  of  the  screw,  or,  more  definitely,  the  backward  slip,  and 
may  be  defined  as  the  distance  which  a  cylinder  of   water, 
of  the  same  diameter  as  the  screw,  has  been  pushed  backward 
while  propelling   the   vessel   forward.     This  slip,  usually  ex- 
pressed as  a  per  cent,  of  the  pitch,  is  then  called  the  coefficient 
of  slip. 

Thus,  suppose  a  screw  vessel  to  pass  over  a  measured  mile, 
with  200  revolutions  of  a  screw  of  30  ft.  pitch.  The  advance 
of  such  a  screw  in  a  solid  nut  being  30  ft.  for  each  revolution, 
would  be  6,000  ft.  in  200  revolutions.  But  176  x  30=5,280=1 
mile.  Hence,  in  the  200  revolutions,  there  has  been  a  slip  of 
24  re  volutions =720  ft.  That  is,  the  co-efficient  of  slip=1fift>(r 
=12  per  cent,  of  the  advance  due  to  the  pitch. 

169.  That  radial  edge  of  a  blade  which  first  enters  the  water 
is  the  forward  or  leading  edge.     That  which  last  enters  is  the 
after,  following,  or  trailing  edge. 

The  central  support  of  the  blades  is  the  hub  or  boss. 


Lateral  Slip. 

170.  In  the  case  of  a  screw,  working  in  a  fixed  nut,  there  is 
not  only  no  motion  of  the  nut  in  the  direction  of  the  axis  of  the 


218  ELEMENTS   OF 

screw,  but  there  is  no  rotation  of  the  nut.  But  in  the  case  of  a 
screw  propeller,  the  yielding  character  of  the  water  or  fluid 
nut,  in  which  the  screw  works,  occasions  not  only  a  backward 
slip,  but  a  lateral  one.  That  is,  the  friction  of  the  blades 
against  the  water,  and  their  lateral  pressure  also,  communicate 
a  measure  of  rotary  motion  to  the  column  of  water  in  which  the 
screw  acts. 

Thus  a  centrifugal  force  is  developed  which  results  in  a  cer- 
tain amount  of  lateral  dispersion,  or  tendency  to  it,  in  the 
cylinder  of  water  acted  upon  by  the  screw. 

171.  Screws  have  been  made  with  the  blades  curved  bac/cward 
to  confine  the  water,  and  propel  it  rearward  with  uiidimished 
diameter,  equal  to  that  of  the  screw.  But  other  makers  have 
curved  the  blades  forward  to  secure  other  supposed  desirable 
results,  so  that,  on  the  whole,  a  simple  screw  is  considered  by 
others  still,  as  good  a  form  as  any  for  a  propeller. 

These  modifications  will  not,  therefore,  be  discussed  at  pre- 
sent. 


172.  Let  S,  Fig.  90,  be  a  screw  working  in  a  nut,  N".     Let 
this  nut  be  capable  of  sliding  backward  or  forward  on  the  car- 


<  PCM 

*  numb 

\        \ 

cz 

c                             \ 

\                             \  \ 

J) 

FIG.  90. 

riage,  C,  and  let  C,  likewise,  be  arranged  to  slide  on  the  fixed 
bed,  D.    Now — 

First,  let  all  parts  be  stationary  except  the  screw,  which  sup- 
pose to  have  a  pitch  of  10  ft.  One  revolution  of  it  will  then 
advance  its  point,  P,  10  ft.  This  corresponds  to  the  case  of  a 
screw  vessel  moving  in  smooth  water  and  witti  no  slip,  under 
the  action  of  the  screw  alone,  a  case  probably  never  fully  real- 
ized. 


h 


MACHINE   CONSTRUCTION   AND   DRAWING.  219 

Second,  while  S,  in  making  one  revolution,  advances  10  ft., 
let  N  move  backward  2  ft. 
The    point,   P,   will  then      ,.  +10 

have  advanced  in  spacej 
Fig.  91,  but  (+10) -2  ft. 
=  8  ft.  This  corresponds 
to  the  usual  case,  where 

the  retreat  of  the  nut  represents  the  distance  which  the  water  is 
pressed  or  displaced  backward,  in  a  horizontal  cylindrical  col- 
umn of  a  diameter  about  equal  to  that  of  the  screw  ;  while  the 
latter  makes  one  revolution.  This  2  ft.  then  represents  the  slip ; 
in  this  case  20  per  cent. 

Third,  the  last  conditions  being  still  retained,  let  the  car- 
riage C  move  forward  3 
ft.     Then   the   point   P      f 
will  advance  in  space  10      k          +10 
ft.,  due  to  one  revolution       ,   ,   ,   ,     ,    ( 
of  the  screw,  minus  2  ft.      ' 
due  to  the  retreat  of  the 
nut,  plus  3  ft.,  Fig.  92,  PIG  ^ 

due  to  the  simultaneous 
advance  of  the  carriage  containing  the  nut  =10  —  2  +  3  =11  ft. 

173.  This  corresponds  to  the  phenomenon,  actually  observed, 
of  an  advance  of  the  vessel,  in  one  revolution  of  the  screw, 
greater  than  the  pitch  of  the  screw,  i.  e.,  greater  than  the  ad- 
vance of  the  screw  would  be,  through  a  solid  nut,  in  one  revo- 
lution. 

This  excess  is  called  negative  slip.  And,  as  in  the  above 
model,  it  would  require  the  same  force  to  turn  the  screw, 
whether  the  carriage  moved  or  not,  so  a  vessel  revealing  nega- 
tive slip  is  not  really  dragging  her  screw,  but  is  propelled  by  it. 
Negative  slip  may  arise  from  a  vessel's  moving  in  a  current  which 
itself  moves  forward  faster  than  the  screw  presses  the  water 
backward.  The  carriage,  therefore,  in  the  first  two  cases  repre- 
sents still  water,  and  in  the  third  case  either  a  current,  as  just 
described,  or  a  local  current  created  by  the  friction  of  the  ves- 
sel and  carried  along  with  it,  or  by  the  rush  of  water  from  the 
rearward  into  the  partial  vacuum  at  the  stern,  when  the  latter 
is  quite  blunt,  as  some  think,  or  a  favoring  wind  capable  of  propel- 
ling the  vessel  faster  than  the  screw  repels  the  water,  or,  finally, 
any  cause  which  advances  the  ship  more  than  the  slip  retards  it. 


Z2U  ELEMENTS   OF 

In  the  case  supposed  of  the  blunt  stern,  the  screw,  instead  of 
literally  pushing  a  column  of  water  rearward,  is  itself  pushed 
along  by  water  rushing  against  it  in  the  direction  of  the  vessel's 
motion.  Lateral  slip  also  tends  to  the  production  of  a  partial 
vacuum  behind  the  screw,  which  would  further  invite  this 
inflow  in  the  line  of  the  axis. 

174.  The  slip,  i.  e.,  common,  or  backward,  varies  up  to  45 
per  cent.,  according  to  the  model  of  the  vessel ;  the  ratio  of  its 
immersed  section  to  the  area  of  the  circle  described  by  the 
outermost  point  of  the  screw  blade ;  the  pitch  and  length  of  the 
screw,  etc.  Hence  quite  a  strong  favoring  wind,  acting  on 
sails,  or  a  current,  may  not  always  overcome  the  slip  but  may 
only  reduce  it. 

Thus,  if  a  screw  of  10  feet  pitch,  while  revolving  once,  ad- 
vance a  vessel  but  6  feet  in  the  same  time,  the  slip  is  40  per 
cent.  But  if  a  breeze  or  current  would  advance  the  ship  2^ 
feet  in  the  same  time  the  total  advance  would  be  8%  feet,  and 
the  apparent  slip  1^  feet,  or  only  15  per  cent,  of  the  pitch. 

We  thus  see  the  importance  of  these  extraneous  conditions  of 
wind  and  current  being  the  same  during  the  progress  of  experi- 
ments on  different  vessels  and  screws. 

It  is  stated  to  be  true,  within  usual  limits,  that  as  the  pitch  of 
a  series  of  screws  is  increased  in  geometrial  progression,  their 
slip  will  increase  in  arithmetical  progression,  for  all  lengths  of 
screw,  other  things  being  the  same. 

But,  interesting  as  the  subject  is,  we  must  stop  somewhere, 
and  therefore  refer  to  the  extended  work  of  Bourne  on  the 
screw  propeller,  for  further  details  based  on  the  numberless 
tabulated  experimental  results  given  by  him. 


Irregular  Screws. 

175.  These  are  screws,  the  acting  surfaces  of  whose  blades  are 
other  than  common  right  helicoids.  They  are  of  two  general 
classes,  first,  those  of  expanding  pitch,  and  second,  those  of 
variable  pitch. 

Screws  of  merely  expanding  pitch  have  fixed  blades,  as  in 
the  plain  or  common  screw.  Those  of  variable  pitch  have 
movable,  that  is,  adjustable  blades,  whose  pitch  may  be  uniform 
or  expanding. 


MACHINE   CONSTRUCTION   AND   DEAWING.  221 

176.  Expanding  pitch  is  either  simple  or  compound.     Simple 
expanding  pitch,  again,  is  of  two  kinds.   First,  if  it  increase  in 
a  direction  parallel  to  the  axis,  as  in  case  of  a  cylindrical  stair- 
case, becoming  steeper  as  it  ascends,  it  is  an  axially  expanding 
pitch.     Such  pitch  increases  from  the  entering  to  the  trailing 
edge  of  the  blade  (169),  that  is,  it  is, greatest  at  the  latter  line. 
Second,  to  illustrate  by  the  circular  stairs  again,  suppose  the 
edges  of  the  steps  to   be   curved  upward  or  downward,  the 
height  of  each  step  would  be  greater  or  less,  respectively,  the 
further  it  was   from   the   axis;   but  let  all  the   steps   be   of 
equal  height,  measured  at  the  same  distance  from  the  axis, 
the  screw,  of  similar  form,  would  have  a  uniform  pitch  at  any 
one  distance  from  the  axis,  but  the  pitch  at  different  distances 
from  the  axis  would  be  different.     This  is  radially  expanding 
pitch.   The  generatrix  might  also  be  a  straight  line,  with  radially 
expanding  pitch,  moving  upward,  for  example,  so  that  any  point 
of  it  out  of  the  axis  would  have  a  greater  pitch  than  at  the  axis. 

177.  Compound  expanding  pitch  is  a  combination  of  both 
axial  and  radial  expanding  pitch  in  the  same  screw.     This  is 
illustrated  by  the  stairs,  by  conceiving  the  heights  of  the  steps  at 
the  axis  to  increase  (or  diminish),  while  the  heights  at  the  cir- 
cumference should  increase  (or  diminish)  faster  than  at  the  axis. 
Then  the  helix,  at  any  given  distance  from  the  axis,  would  be 
steeper  and  steeper  (or  the  reverse)  as  it  ascended,  and  the 
helix  at  the  circumference  would  have  the  greatest  (or  least) 
pitch,  though  the  greatest  circular  path  swept  over  by  it  might 
make  it  less  steep  in  both  cases  than  at  points  nearer  the  axis. 

We  will  now  illustrate  in  a  simple  manner  the  several  suc- 
cessive elements  of  the  formation  of  such  forms  of  helicoidal 
surface  as  are  employed  in  the  designing  of  screw  propellers, 
and  shall  then  proceed  to  the  representation  of  these  organs  in 
their  practical  working  forms. 


PROBLEM  XI. 
To  Construct  a  Helix  of  Uniform  Pitch  and  Radius. 

Let  the  axis  of  the  helix  be  vertical.     Then  O— O'O",  PL 
XXVL,  Fig.  1,  will  represent  such  an  axis ;  and  the  circle  with 


222  ELEMENTS   OF 

radius  Oa,  will  be,  at  once,  the  horizontal  projection  of  the 
helix  and  of  the  vertical  cylinder  with  axis  O — O'O",  upon 
which  it  lies. 

The  construction  is  based  immediately  upon  the  definition 
(152).  Thus,  the  division  of  the  circle,  adgk,  into  equal 
parts,  indicates  the  uniform  rotary  movement  of  the  generating 
point,  a — a',  around  the  axis ;  and  the  division  of  O'O"  into 
equal  parts  indicates  the  uniformity  of  the  axial  motion. 

In  the  figure,  O'O"  is  taken  as  the  pitch  of  the  helix,  by 
dividing  it  into  the  same  number  of  equal  parts  as  are  found  on 
the  circle  adgk. 

Observe  that  the  equal  parts  here  spoken  of,  are  made  so  for 
convenience.  All  that  is  necessary  is  that  the  parts  on  O'O" 
should  be  proportional  to  the  homologous  ones  on  adgTt.  Also 
O'O",  the  pitch,  is  of  any  length,  taken  at  pleasure. 

This  being  understood,  let  the  helix  leave  the  horizontal 
plane  at  #,  in  a  forward  and  upward  direction.  Then  a  will  be 
projected  at  a',,  on  the  ground  line  ;  ft,  at  b',  in  the  horizontal 
plane,  BJ',  etc. ;  as  is  obvious  on  inspection  of  the  figure. 

The  foremost  point,  dd',  of  the  helix  appears  in  vertical  pro- 
jection on  the  vertical  projection  of  the  axis  ;  and  so  does  the 
hindmost  one,  jj'. 

By  joining  the  points  a'Vc' g'  —  a",  as  shown,  we  get  the 

vertical  projection  of  the  helix,  whose  horizontal  projection  is 
the  circle  of  radius  Oa. 

Remarks. — a — The  figure  is  very  fully  lettered,  to  assist  in 
apprehending  the  real  position  of  the  several  points  of  the  helix. 

b — Had  the  generatrix,  aaf,  proceeded  backward  and  upward, 
bb'  would  have  appeared  at  lbf. 

178. — The  drawing  of  any  irregular  surface,  as  a  ship's  sides, 
is  often  called  "  laying  down  its  lines." 

Every  surface  is  composed  wholly  of  lines  of  some  kind.  The 
lines,  distinctively,  of  a  given  surface,  are  those  which  are  most 
clearly  characteristic  of  it,  that  is,  those  which  most  readily 
enable  the  mind  to  conceive  of  it  from  a  diagram. 

A  screw  propeller  is  mainly  bounded  by  a  cylinder,  having 
the  same  axis  as  the  propeller,  and  by  two  parallel  planes  per- 
pendicular to  that  axis.  "We  will  therefore,  as  a  preliminary 
construction,  give  the  projections  of  a  common  right  helicoid  ; 
first,  as  represented  by  its  straight  elements ;  second,  by  its 
helical  lines. 


MACHINE   CONSTRUCTION   AND   DRAWING.  223 

Note. — All  the  figures  of  helices  and  helicoids,  on  PL  XXVL, 
should  be  drawn  by  the  student  at  least  twice  as  large  as  there 
shown,  and  with  a  full  descriptive  title  for  each. 


PROBLEM  XII. 

To  construct  the  projections  of  so  much  of  a  common  right 
helicoid,  as  is  generated  by  the  radius  of  a  vertical  cylinder. 

Let  O— O'O",  PI.  XXYL,  Fig.  1,  be  the  axis,  and  the  circle 
of  radius  Oa,  the  plan  of  the  given  cylinder. 

The  circle  Oa,  and  the  axis,  are  each  equally  divided,  and  the 
helical  directrix  (147)  acfk — a'c'f'lda" ,  is  constructed  as  in  the 
last  problem.  Then  by  the  definition  of  the  right  helicoid,  the 
horizontal  lines  aO — a'O' ;  bO — 5'B' — cO — c'C' 
aO — a"O"  represent  the  helicoidal  surface  by  its  straight 
" lines"  or  elements,  and  for  one  complete  convolution  about 
the  axis  O— O'O/' 

Remark. — To  show  the  helical  band  which  would  be  in 
eluded  between  two  concentric  cylinders,  draw  any  circle  with 
centre  O,  and  project  its  intersections  with  the  radii  Oa,  etc., 
produced  if  desired,  upon  the  indefinite  horizontal  lines  O'a', 
B'J',  CV,  etc.,  as  before.  See  also  Prob.  XI. 


PROBLEM  XIII. 

To  construct  the  projections  of  a  common  right  helicoid,  which 
is  generated  by  the  diameter  of  a  vertical  cylinder. 

Let  O— O'O",  PL  XXVI.,  Fig.  2,  be  the  axis,  and  Aa— AV, 
the  initial  position  of  the  diameter  of  the  given  cylinder ;  and  let 
O'O"  be  the  pitch  of  the  helicoid.  Divide  the  circle  of  radius 
Oa,  and  the  pitch  O'O",  each  equally,  as  in  the  last  problem. 
Indefinite  horizontal  lines,  Aa — A'a' ;  A,#, — A/a/  -  -  -  Asa3 
— A/«3',  etc.,  through  the  divisions  on  O — O'O",  will  then  be 
indefinite  elements  of  the  required,  helicoid,  and  they  will  be 
limited  as  required,  by  considering  the  line  Aa — AV  as  the 
generatrix,  and  as  revolving  in  this  case,  so  that  as  AA'  moves 
upward  and  forward,  aa'  moves  upward  and  backward.  Hence 


224:  ELEMENTS   OF 

AA'  describes  the   helix  AA3A6A9AU— A'A/A/A/A,/  and 

aaJ  describes  the  opposite  helix  aa3ata10 — a'a^'a^'aj. 

Remark. — Returning  to  Fig.  1 :  Any  radius  will  generate  a 
helicoid,  thus  if  Oa— O'a' ;  Od—O' ;  Og— O'A'  and  O;— O', 
four  separate  radii  of  the  base  of  the  given  vertical  cylinder 
be  taken  as  generatrices,  their  simultaneous  helical  ascension 
will  generate  four  helicoids,  all  like  the  single  one  shown  in 
the  figure. 

PROBLEM  XIV. 

Having  given  either  projection  of  any  element  of  a  helicoid,  to 
find  its  other  projection. 

Let  mO  and  nO,  PI.  XX VI.,  Fig.  1,  be  any  intermediate 
elements,  taken  at  pleasure,  on  a  common  right  helicoid. 

There  are  two  ways  of  finding  their  vertical  projections. 

First.  Project  the  points  m  and  n,  upon  the  vertical  projec- 
tion of  the  helix  containing  them,  as  at  m!  and  n',  and  the  hori- 
zontal lines  mfo'  and  n'v'  will  be  the  required  vertical  projec- 
tions. Conversely,  in  the  same  manner,  having  m'o'  given, 
project  down  m!  at  m,  in  the  horizonal  projection  of  the  helix, 
and  mO  will  be  the  required  horizontal  projection  of  m'o.' 

Second.  From  the  definition  of  the  helicoid,  make  O'o  a 
fourth  proportional  to  the  circumference  adga  /  the  arc  am,  and 
the  pitch  O'O,"  and  o'm'  will  then  be  the  vertical  projection  of 
Om. 

PROBLEM  XY. 

To  represent  a  common  right  helicoid  by  its  helical  "  lines." 

Let  the  concentric  circles  of  radii  Oa,  Oal O#B,  PL 

XXVI.,  Fig.  3,  be  the  horizontal  projections  of  a  series  of  con- 
centric helices,  all  on  the  same  helicoidal  surface,  whose  gene- 
ratrix is  Oa — O'a'.  As  the  required  surface  is  a  right  helicoid, 
all  these  points  of  the  different  helices,  which  are  on  the  same 
radius,  are  at  the  same  height  above  the  horizontal  plane,  the 
axis  O — O'O"  being  vertical,  as  before. 

Hence,  having  taken  any  distance,  O'O",  for  the  pitch,  and 
having  divided  it,  and  the  circles  of  the  plan,  each,  into  the  same 


MACHINE    CONSTRUCTION   AND   DRAWING.  ^lo 

number  of  equal  parts,  project  all  the  points  of  Oa  into  O'#'/ 
those  of  O5  into  B'#',  etc.,  and  join  the  joints  as  a'b'c'f'h'  and 
a/^y/A/,  etc.,  of  the  separate  helices  as  shown.  This  will  give 
the  vertical  projections  of  the  helices,  whose  horizontal  projec- 
tions are  the  concentric  circles  with  their  centre  at  O.  The  two 
projections  of  these  helices,  then  represent  to  the  eye  the  heli- 
coidal  surface. 

Here  observe,  carefully,  that  the  steepness  of  any  given  helix 
is  not  to  be  confounded  with  its  pitch.  All  the  helices  just  de- 
scribed have  the  same  pitch,  O'O",  but  their  steepness  decreases 
from  the  axis,  where  it  is  greatest,  being  vertical,  to  the  helix 
whose  radius  is  infinite,  where  it  would  be  least,  being,  sensibly, 
=  0,  for  the  height  O'O"  is  as  nothing  compared  with  a  cir- 
cumference of  infinite  radius  (163). 


PROBLEM  XVI. 

To  construct  the  "  lines"  of  a  helicoid,  made  by  its  intersection 
with  any  plane  parallel  to  its  axis. 

Let  PQ,  PL  XXVI.,  Figs.  1  and  2,  be  the  horizontal  traces 
of  vertical  planes  cutting  the  helicoids.  Since  these  planes  a~e 
vertical,  their  horizontal  traces,  PQ,  are  also  the  horizontal  pro- 
jections of  all  points  and  lines  in  them.  Hence  d'"qst  is  at 
once  the  horizontal  projection  of  the  required  intersection  in 
Fig.  1 ;  and  PmrQ,  in  Fig.  2.  In  both  figures,  project  up  the 
points  d'",p,q,  etc.;  m,n,  etc. ,  upon  the  vertical  projections  of 
the  elements  O^,  O<?,  etc.,  and  OAn  OA2,  etc.,  upon  which  they 
are  found. 

"VYe  thus  find  on  Fig.  1,  d'p'  .  .  .  £',  and  on  Fig.  2,  m'n'p'q', 
for  the  vertical  projections  of  the  required  intersections. 

The  elements  Om — o'm'  and  Oft — v'n',  Fig.  1  (See  Prob. 
XIV.),  are  parallel  to  the  plane  PQ,  and  hence  never  intersect 
it.  Likewise,  the  more  nearly  parallel  an  element,  as  Oc — C'c',. 
is  to  PQ,  the  further  from  the  axis  will  it  intersect  PQ.  That 
is,  those  points  of  the  curve  d's't',  which  are  in  the  elements 
om'  and  v'n,'  are  infinitely  distant  from  the  axis.  In  other 
words,  this  curve  will  be  tangent  to  those  elements  at  an  infinite 
distance ;  hence  the  latter  are  said  to  be  asymtotes  to  the  curve 
d's't'u'. 
15 


226  ELEMENTS   OF 

It  is  now  evident  that  such  lines  as  the  one  just  described  are 
quite  inferior  to  the  radial  and  helical  ones  in  clearly  represent- 
ing the  form  of  the  helicoidal  surface. 

Also  that  if  we  trace  any  kind  of  line  on  either  projection 
of  the  helicoid,  its  other  projection  would  be  found  by  noting 
its  intersections  with  the  elements,  or  helices,  in  the  projection 
on  which  the  line  is  traced,  and  by  projecting  these  points  into 
the  other  projections  of  the  same  elements  or  helices,  and  join- 
ing them. 

PROBLEM  XVII. 

Having  given  either  projection  of  any  point  upon  a  helicoid,  to 
find  its  other  projection. 

We  will  describe  the  general,  and  two  particular  methods  of 
solving  this  problem. 

The  General  Method. — Construct  any  line  upon  the  helicoidal 
surface  and  passing  through  the  supposed  point.  The  required 
projection  of  this  point  will  be  on  the  like  projection  of  this  aux- 
iliary line.  Thus,  in  PL  XXVL,  Fig.  1,  if  the  horizontal  pro- 
jection of  the  point  were  given  anywhere  on  PQ,  its  vertical 
projection  would  be  found  by  projecting  it  upward  upon  d'p'q't'. 

Particular  methods.— First.— Let  m,  PI.  XXVL,  Fig.  2,  be 
the  given  projection.  Then,  by  Prob.  XIV.,  construct  the  pro- 
jections, Om — o'm',  of  an  element  through  it,  and  m'  will  be 
on  o'm'.  Likewise  m',  if  given,  would  be  projected  upon  Om, 
to  find  m. 

Second. — Construct  the  helix  containing  the  supposed  point, 
and  the  required  projection  of  the  point  will  be  on  the  like  pro- 
jection of  the  helix.  Thus,  having  given  &,  PL  XXVL,  Fig.  3, 
construct  the  helix,  daft — d'f\  through  it,  and  k'  will  be  pro- 
jected from  ~k  upon  d'f\. 

PROBLEM  XVIII. 
To  develope  one  or  more  given  helices. 

When,  as  in  PL  XXVL,  Fig.  4,  we  have  among  straight  lines 
the  relation 

AM  :  ME  : :  AH  :  HK 

the  line  AK,  containing  the  extremities  of  the  parallels,  ME, 
HK,  etc.,  is  straight. 


MACHINE   CONSTRUCTION   AND   DRAWING.  227 

Now  with  this  the  helix  agrees,  for  the  distances  db,  ac,  etc., 
from  a,  Fig.  3,  on  the  base  of  the  cylinder  on  which  the  helix 
lies,  being  proportional  to  the  heights  of  the  corresponding  points 
b',  G'J  etc.,  of  the  helix  above  that  base,  it  follows,  that  when  the 
convex  surface  of  the  cylinder  is  unrolled,  and- made  flat,  the 
base  will  become  a  straight  line  as  AG,  Fig.  4,  the  successive 
heights  will  be  parallel  as  at  ME  and  HK,  and  the  development 
of  the  helix  will  be  straight,  as  at  AF. 

Hence,  to  develope  a  half  convolution  adf- — a'd'f  of  the 
helix,  make  AG  equal  to  the  semi-circle  adf,  and  GF— Ay, 
and  AF  will  be  the  required  development. 

Again :  as  the  common  helix  has,  by  its  definition,  a  uniform 
angle  of  inclination  to  the  horizontal  plane,  the  parts  ab,  be,  etc., 
being  equal  in  horizontal  projection,  are  equal  in  space  also. 
Hence  the  same  parts  are  equal  in  development.  That  is  AB, 
BC,  CD,  etc.,  Fig.  4,  are  the  equal  developments  of  the  equal 
parts  ab — a'b\  be — I'e',  etc.,  of  the  helix. 

Making  OA1=NF1=the  quadrant  a,da  and  drawing  AjF,. 
this  line  is  the  development  of  a^/j — a^'d'f^'. 

In  a  precisely  similar  manner,  all  the  helices  of  Fig.  3  are  de- 
veloped at  A2F2,  etc.,  in  Fig.  4,  and  all  intersect  at  D. 

Instead  of  laying  off  a  quadrant  each  side  of  O,  Fig.  4,  a  semi- 
circumference  for  each  helix  might  have  been  laid  off  from  A. 
making  that  the  common  point  for  all  the  developments. 

PROBLEM  XIX. 

From  the  circular  projection,  and  development  of  a  helix,  to 
construct  its  spiral  projection. 

Let  adf^S,  PI.  XXVI.,  Fig.  3,  be  the  given  circular  projec- 
tion, and  AF,  Fig.  4,  be  the  given  development  of  a  half  convo- 
lution of  the  same  helix. 

Divide  adf  and  AF,  each  into  the  same  number  of  equal 
parts.  Then,  by  the  properties  of  the  helix  already  explained, 
it  is  clear  that  any  point,  as  <?',  of  the  vertical  projection,  is  at 
the  intersection  of  a  perpendicular  to  the  ground  line  Aa',  from 
c',  with  a  parallel  to  the  ground  line  from  C. 

Helices  are  often  constructed  in  this  way,  especially  if  the 
angle  of  inclination  FAG  be  given.  See  also  PI.  XXXI., 
Fig.  3. 


228  ELEMENTS    OF 

PROBLEM  XX. 

To  construct  a  helicoid  of  axial  expanding  pitch.  Try  means  of 
its  helical  lines. 

First  Illustration.— Let  O— O'O",  PI.  XXVI.,  Fig.  5,  be  the 
axis  of  such  a  helicoid,  and  let  OA — O'A'  be  the  initial  position 
of  its  generatrix,  and  let  the  successive  ascents  of  this  line,  cor- 
responding to  the  equal  angular  motions  AB,  BC,  etc.,  be  in 
arithmetical  progression.  Thus,  on  a  small  figure  like  this,  let 
Mm=4-50ths  of  an  inch ;  wio=5-50ths ;  6>r=6-50ths,  etc., 
and  draw  horizontal  lines  through  these  points.  Then  project 
up  A  at  A' ;  B  at  B',  on  the  line  through  m  ;  C  at  C',  on  the 
line  through  o,  etc.,  until  KK',  on  the  line  through  M',  is 
reached.  The  concentric  helix,  beginning  at  LI/,  is  projected 
upon  the  same  lines.  Thus  we  find  two  helices  of  the  same 
axial  expanding  pitch,  the  successive  ascents  of  whose  generatrix 
have  equal  differences.  The  helical  band  A'L' — K'L"  is  thus 
one  of  axial  expanding  pitch,  which  obviously  becomes  steeper 
as  it  ascends. 

Second  Illustration. — Let  the  generatrix,  Oa- — O'a',  in  the 
same  figure,  5,  ascend  so  that  its  successive  rises,  ~Nn,  nk,  kp, 
etc.,  shall  be  in  geometrical  progression.  In  the  figure,  ~Nn  = 
4-50ths  of  an  inch,  and  the  ratio  was  Jive-fourths.  Hence  the 
spaces,  from  1ST  upward,  have  a  constant  ratio  instead  of  a  con- 
stant difference,  as  on  MM'.  Drawing  horizontal  lines  through 
the  points  n,  k,  etc.,  project  a  at  a!,  5  at  b'  on  the  horizontal  line 
through  n;  c  at  c  on  to',  etc.  D'  and  d  sensibly  coincide,  be- 
cause, in  using  so  small  distances  on  MM7  and  NN',  the  differ- 
ence between  the  two  progressions  does  not  so  soon  appear, 
though  above  D,  it  soon  becomes  apparent,  and  the  new  helicoid 
ad-g-si — a'g'-s'i'  is  steeper  at  i',  the  eighth  point  from  K",  than 
the  former  one  was  at  K7,  the  tenth  point  above  M. 

PROBLEM  XXI. 
To  develope  ttiefour  helices  last  drawn. 

For  the  first,  or  arithmetical  helicoid,  let  the  vertical  element 
at  d  of  the  cylinder  on  which  lies  the  helix,  PI.  XXYI.,  Fig.  5, 
be  placed  in  the  paper  at  d'd",  Fig.  6.  Then  make  d'a=d'A  = 
the  arc  da,  or  6?A,  Fig.  5,  and  let  it  be  similarly  divided  on  both 


MACHINE    CONSTRUCTION    AND    DRAWING.  229 

figures.  d'c=dc  in  Fig.  5,  Af=Af,  etc.  Then  make  vertical 
lines  at  those  points,  and  project  g'y  Fig.  5,  on  Ag,  at  g,  Fig.  6 ; 
y,  Fig.  5,  on  JT,  Fig.  6,  and  so  on,  and  the  curve,  ag,  will  be  the 
development  of  the  expanding  helix  ag — a'g '. 

In  like  manner  are  found  qdt,  the  development  of  qt — q'D't'  • 
AG,  the  development  of  AG — A'G',  and  LZ,  the  development  of 
12 — L'l'  in  Fig.  5.  The  two  latter  helices,  being  on  the  back 
half  of  the  cylinder,  d'd"  represents,  for  them,  the  vertical  ele- 
ment at  D,  each  way  from  which  the  cylinder  is  developed  into 
the  paper. 

PROBLEM  XXII. 

To  make  the  projections  of  a  helicoid  of  radially  expanding 
pitch. 

PI.  XXVL,  Fig.  7,  where,  for  convenience,  the  plan  is  over 
the  elevation.  Here  the  pitch  is  proportional  to  the  distance 
from  the  axis,  O — O'O"  and  the  initial  position  of  the  genera- 
trix is  OA — O'A',  which  after  a  helical  semi-revolution,  comes 
to  the  position  OC — B'C',  (176)  where  B',  on  CB',  happens  to  co- 
incide with  B'  as  the  vertical  projection  of  B,  a  point  in  front 
of  the  axis,  on  the  outermost  helix. 

Then  C'J  is  the  pitch  of  the  outer  helix,  from  AA',  in  a  half 
revolution ;  G'K,  that  of  the  helix  from  EE' ;  c'L,  that  of  the 
helix  from  aa' /  </'M  that  of  the  helix  from  ee\  and  O'B'  that 
of  the  axis,  considered  as  the  inmost  helix ;  all,  in  a  half  revo- 
lution. Then  construct  each  of  these  helices,  by  dividing  the 
half  pitch  of  each  into  as  many  equal  parts  as  are  in  the  horizon- 
tal projection  of  its  half  revolution.  Thus,  C'J  and  ABC,  are, 
in  the  figure,  each  divided  into  six  equal  parts. 

Observe  that,  as  shown  by  this  example,  the  several  helices  do 
not  cross  the  axis,  in  vertical  projection,  at  the  same  point,  as 
they  do  in  all  right  helicoids,  Figs.  1,  2  and  3,  whether  the 
pitch  be  uniform  or  expanding  axially. 

Yariations  from  this  figure,  which  the  student  should  now 
make  for  himself,  on  a  large  scale,  are,  to  make  the  generatrix 
B'C',  a  constant  curve,  as  AB  or  AC,  Fig.  8,  all  points  of  which 
shall  have  the  same  uniform  pitch.  Also  to  make  the  pitch  at 
each  point  of  B'C'  greater  or  less  than  proportional  to  its  dis- 
tance from  the  axis.  The  series  of  distances  as  J/>,jp<?,  etc., 
upward  from  O',  M,  L,  K,  and  J,  will  then  each  be  in  arithme- 


230  ELEMENTS   OF 

tical  or  geometrical  progression,  as  at  MM'  or  at  XX',  in  Fig. 
5,  but  with  a  larger  or  smaller  common  difference,  or  common 
ratio,  the  farther  each  is  from  the  axis. 

In  Fig.  7,  the  different  pitches  O'B',  M/,  Lc',  etc.,  are  in 
arithmetical  projection,  they  having  equal  differences. 

To  obtain  pitches  in  geometrical  projection  let  OA  and  OB, 
PI.  XXYL,  Fig.  9,  be  two  given  lines.  Then  OC  is  a  third 
proportional  to  OA  and  OB,  and  by  a  similar  construction, 
joining  AC  and  drawing  a  parallel  BD,  we  find  OD,  a  fourth 
proportional  to  OA,  OB,  and  OC.  Likewise  we  can  find  a 
fourth  proportional  to  OB,  OC,  and  OD,  and  so  on,  forming  a 
geometrical  progression.  The  curve,  AD,  Fig.  10,  joining  the 
outer  points  of  these  lines,  when  they  are  placed  as  equidistant 
radii,  will  be  a  logarithmic  spiral ;  all  equidistant  radii  of 
which  are  terms  in  a  geometrical  progression.  TVe  can  then 
substitute  such  radii  for  JC',  KG',  etc.,  in  Fig.  7. 

If  AB,  Fig.  8,  revolve  uniformly  around  CB  as  an  axis,  and 
so  that  all  its  points  move  with  the  same  uniform  velocity, 
parallel  to  CB,  it  will  generate  a  screw  of  uniform  pitch,  with 
a  curved  generatrix. 

If  all  points  of  AB  move  equally  faster  and  faster  in  the 
direction  of  the  axis,  while  still  revolving  uniformly,  AB 
will  generate  a  screw  with  asdally  expanding  pitch,  but  uni- 
form radial  pitch.  If,  again,  all  points  of  AB  have  an  accele- 
rated motion,  but  if  the  velocity  of  each  point  increases  faster, 
the  further  it  is  from  the  axis,  the  screw  ha&  then  a  radially 
expanding  pitch,  and  AB  will  be  of  variable  form,  becoming 
more  curved  as  it  proceeds. 

In  all  these  cases,  the  several  concentric  helices  will  cross  the 
axis  CB  (in  projection)  at  different  points,  as  in  Fig.  7 ;  in  the 
first  two  cases,  merely  because  the  generatrix  is  curved  ;  in  the 
last,  for  the  additional  reason  that  the  pitch  expands  radially. 

The  student  will  learn  more,  essentially,  about  various  pro- 
pellers, by  carefully  constructing  the  last  three  cases,  than  by 
drawing  the  propellers  themselves,  without  such  separate  drill 
on  their  essential  differences. 

PROBLEM  XXIII. 

To  develope  the  helices  shown  in  the  la.st  problem. 
In  PI.  XXVI.,  Fig.  11,  A'J  =  ABC  in  the  plan,  Fig.  7,  and 


MACHINE   CONSTRUCTION   AND   DRAWING.  231 

JC  =  JC'  in  the  elevation  of  the  latter  figure.  Hence  CA'  is 
the  development  of  the  half  turn  ABC — A'B'C',  of  the  outer 
helix.  Likewise,  KE  =  semicircle  EFG,  and  GK  =  G'K  from 
the  elevation.  Then  GE  is  the  development  of  the  helical  arc 
EFG — E'G'.  From  this  description  the  rest  of  the  develop- 
ment can  be  drawn. 

179.  The  preceding  general  problems  furnish  all  the  means 
necessary  for  showing  how  to  construct  the  projections  of  the 
acting  faces  of  the  blades  of  screw  propellers,  these  faces 
always  being  portions  of  helicoids  of  some  kind.  The  term 
pitch,  is  applied  to  the  propeller  in  the  same  sense,  and  with 
the  same  variations,  as  to  the  helicoids  already  explained. 

The  backs  of  the  blades  are  the  surfaces  which  result  from 
giving  such  thicknesses  to  the  blade  at  different  distances  from 
its  axis,  as  are  found  to  be  necessary. 

PROBLEM  XXIV. 

To  construct  the  projections  of  the  acting  faces  of  a  four-Haded 
common  screw  propeUer. 

The  axis  of  a  propeller  in  its  working  position  being  hori- 
zontal, the  screw  would  naturally  be  shown  in  two  elevations. 
Therefore  let  the  plan  in  PL  XXVI. ;  Fig.  3,  serve  as  one  of 
two  elevations  for  Fig.  12,  and  let  the  full  circle,  with  radius 
Cm,  be  the  hub  of  the  screw.  Also  let  DBO,  MOJ,  cOe,  and 
KOE,  be  the  four  blades,  as  seen  in  end  elevation.  Construct, 
by  Problem  XV.,  the  indefinite  helices,  beginning  at  c,  c' ;  K,K' ; 
D,  D'  and  M,  M' ;  whose  pitch^D'D"".  These  are  respect- 
ively, in  side  elevation  cWVK"E"  .  .  .  . ;  K'E'B' 'a"  /  D'^'B'5" 
d'"D"" ;  and  Wb'd"a".  Make  D'B',  the  length  of  the  wheel, 
so  that  B,  B'  and  D,  D'  shall  be  equidistant  from  vertical 
planes  at  dg  and  d'g ' .  Then,  having  projected,  as  in  other 
cases,  the  concentric  helices,  as  nmr,  of  intersection  with  the 
hub,  we  have  tymr^BgD — n'm'n" ,  D'^'B',  for  the  helicoidal 
face  of  one  blade,  os~M.b — oYM'i'  for  that  of  another,  etc. 

If  this  screw  revolve  in  the  direction  of  the  arrows,  the  re- 
action of  the  water,  supposed  to  be  at  the  right  of  it,  would 
propel  the  vessel,  whose  hull  would  be  at  the  left  of  it,  in  the 
direction  of  arrow  N. 


232  ELEMENTS    OF 

M"5"  is  identical  in  form  with  M'5',  but  is  an  arc  of  the 
same  helix  with  D'i?'B'.  Hence  the  right-hand  wheel,  D"d", 
correctly  represents  the  left-hand  one,  D'd',  after  the  latter  has 
made  just  a  quarter  revolution. 

EXAMPLE  LIT. 

To  represent  variously  limited  propeller  blades,  with   their 
concentric  and  radial  sections. 

PI.  XXVII. ;  Figs.  2-7.  Fig.  2  is  a  common  end  elevation 
of  the  three  screws  Figs.  3,  4,  and  5  ;  in  all  of  which  the  pitch 
is  the  same,  for  convenience  of  comparison. 

1°. — Figs.  2  and  3  are  two  elevations  of  a  common  screw, 
where  ABCD — A'B'E'C'D'  is  identical  in  character  withy'F'G' 
H'A'f/',  PI.  XXIII. ;  Fig.  1,  half  of  whose  horizontal  projec- 
tion is  yFG<7.  Only  that  in  the  latter  figure,  the  difference, 
<?G,  between  the  radii  of  the  inner  .and  outer  cylinders  of  the 
screw,  is  much  less  than  rE — r'E',  PI.  XXVII.,  the  difference 
of  the  radii  of  the  hub,  and  the  cylinder  of  radius  OC,  con- 
taining the  outer  helical  edge,  EEC — B'E'C',  of  a  blade. 

NT — N'P',  etc.,  are  concentric  helices  of  the  blade  AC — 
A'C',  which  is  seen  flatwise  in  both  projections.  Likewise  KL 
— K'L',  FG — F'G',  etc.,  are  concentric  helices  of  the  blade  FH 
— F'J'H'G',  seen  edgewise  in  Fig.  3.  We  see  from  this  that  it 
is  not  a  very  material  error  to  make  J'lF,  K'L',  etc.,  straight; 
but  it  is  quite  wrong  to  make  them  in  the  same  direction  as 
their  developments,  rg',  KSL3,  etc.,  Fig.  6,  by  the  difference  q'h", 
Fig.  3  (for  J'lF)  between  J'A",  the  projection  of  J'lF  on  the 
horizontal  O'B',  and  3'q=rq  Fig.  6.  The  error  of  representing 
XP — N'P',  etc.,  as  straight  in  the  edge  view,  Fig.  3,  of  the  wheel, 
is  now  apparent.  Such  lines  may  be  used  only  as  containing 
the  points,  X,  ~N'  and  P,  P'  on  the  edges  of  the  blade,  and  then 
no  practical  error  will  result.  But  to  view  them  as  represent- 
ing the  helices,  as  NtfP — N"YP  is  entirely  wrong. 

Another  error  consists  in  speaking  of  a  certain  artificial 
figure,  next  described,  as  the  "  development "  of  a  blade, 
though  no  warped  surface  (158)  can  be  developed.  Such  a 
figure  is  made  by  extending  the  chord  KL,  for  example,  till 
equal  to  K'L'  (KSL3),  and  drawing  a  curve  through  its  new  ex- 
tremities and  R.  The  conventional  figure,  formed  by  connecting 
the  like  extremities  of  the  different  chords,  and  which  is  broader 


MACHINE    CONSTRUCTION   AND   DRAWING.  233 

than  the  projection,  FIT,  of  the  blade,  is  sometimes  called  its 
"  development ;"  and  the  curves  having  the  extended  chords  are 
called  the  developments  of  the  helices  KRL — K'L'.  Yet  this 
figure  represents  nothing  real,  and  is  of  no  particular  use. 

2°.  Assumed  form  of  the  side  view  of  a  blade. — Propeller 
blades  may  be  limited  otherwise  than  by  parallel  planes,  as  H'C' 
and  A"B',  Fig.  3.  And,  as  the  form  and  size  of  the  projection, 
A'B'C'D',  shows,  the  assumed  form  of  the  blade  outline  is  made 
on  that  figure,  and  thence  constructed  by  projection,  on  Fig.  2. 

Fig.  4  shows  a  blade  rounded  at  the  outer  corners  and  partly 
straight  as  &tf'g',  and  limited  on  the  side  by  the  line  d'a'.  The 
end  elevation  shown  in  a  light  line  on  Fig.  2,  may  be  found 
by  projecting  points  as  c',  on  given  radii,  over  to  the  other  pro- 
jection of  the  same  radius  as  at  c.  Otherwise,  by  projecting 
points,  as  d'  or  A',  on  any  given  helix,  as  d'i'g'  or  k'j'l',  respect- 
ively, upon  the  other  projection  of  that  helix,  as  on  dig,  at  d, 
or  Jcjl  at  h.  The  points,  ff'  and  gg'  are  taken  on  radii  and  pro- 
jected upon  fb  and  gn. 

To  construct  the  blade,  G"H' V,  Fig.  4,  we  have  only  to  con- 
struct its  helices  in  the  same  way  as  in  Fig.  3,  and  then  to  pro- 
ject points  as  e'd'  or  s'  on  any  helix  of  the  blade  BB"DD"  upon 
the  corresponding  helix  of  the  given  blade.  Thus  e'  on  the  outer 
helix  k'j'l',  is  projected  at  e",  on  the  similar  helix  mm" — m'm'". 

3°.  Propellers  with  Hades  "  bent  back." — This  rather  obscure 
phrase,  may  mean  that  a  blade,  as  GFC'",  PL  XXYII. ;  Fig. 
5,  is  truncated  by  two  cylinders,  concentric  or  not,  and  perpen- 
dicular to  the  paper,  whatever  be  the  nature  of  the  pitch,  and 
the  form  of  the  generatrix.  But  it  should,  and  probably  does, 
mean  that  the  generatrix  is  curved  back  as  at  OrE — HE'", 
Figs.  2  and  5. 

In  this  case,  FG  and  C'"D"'  are  simply  positions  correspond- 
ing with  A'B'  and  C'D'  in  Fig.  3.  of  the  curved  generatrix 
E;"II.  Hence  FG  and  C'"D'"  are  not  circular  arcs,  but  curves, 
whose  ordinates  from  LK  could  be  determined  by  scale,  at 
various  points  on  a  careful  construction  of  large  size. 

4°.  To  construct  the  concentric  sections. — These  are  made  by 
concentric  cylinders,  whose  common  axis  is  perpendicular  to  the 
paper  at  O.  Make  K3,9,  Fig.  6,  equal  to  the  arc,  KRL,  for  ex- 
ample, Fig.  2,  and  sL3  equal  to  O'O",  Fig.  3,  the  pitch  of  a 
blade  ;  then  K3L3  will  be  the  development  of  KL — K'L'.  Xow 
make  K3S"V"L,  at  pleasure,  for  the  section  of  the  back  of  the 


234:  ELEMENTS    OF 

blade,  in  the  same  cylindrical  surface  with  the  helix,  KL — K'L'. 
The  lines  K3.s,  o'U",  etc.,  are  the  same  as  the  traces  A"B',  Uw?', 
etc.,  in  Fig.  3.  In  the  latter,  make  the  lines  through  S'  and  X' 
at  the  same  distance  below  K'  and  L'  as  those  through  S"  and 
X"  are  below  K3  and  L3,  Fig.  6.  Then  project  the  points  S", 
etc.,  of  the  back  of  the  blade  upon  any  line,  AB,  Fig.  6,  par- 
allel to  K3s,  and  transfer  them  to  the  arc  KL  in  Fig.  2,  giving 
the  points  there  numbered.  Finally,  project  the  latter  points  ; 
0,  upon  the  line  A'  B'  at  K' ;  1,  upon  Q'S'  at  S' ;  2,  upon  B'A' 
again,  at  T'S',  see  Fig.  6,  because  T"  and  K3  happen  to  be  on 
the  same  line,  parallel  to  AB ;  etc..  and  we  have  K'S'4X'L'  for 
the  vertical  projection  of  the  section  of  a  blade,  made  by  a 
cylinder  whose  radius  is  OK,  and  whose  axis  is  perpendicular  to 
the  paper  at  O.  In  Fig.  6,  7""  and  H""  are  the  developments 
of  sections  similar  to  the  one  just  described,  at  the  hub,  and  at 
the  outer  edge.  Their  projections  can  be  made  in  the  way  just 
described.  F'",  K2L.,,  and  H"',  Fig.  7,  are  the  three  sections, 
laid  parallel  to  each  other  for  convenient  comparison. 

KjLjR,  shows  the  section  on  KL ;  first,  developed  into  the 
plane  K,L, ;  second,  revolved  about  OI  till  its  edge,  KL,  comes 
into  the  paper ;  third,  revolved  about  Iv,  L,  till  its  whole  sur- 
face is  in  the  paper. 

It  is  here  to  be  noted,  that  as  the  screw  surface  is  warped, 
neither  these  nor  any  other  cylindrical,  nor  any  plane  or  conical 
sections  could  show  a  series  of  perpendicular  thicknesses  of  the 
blade.  For  the  different  tangent  planes  at  points  on  any  one 
helix  would  not  be  parallel  to  any  one  line,  as  in  case  of  a 
cylinder,  where  all  the  tangent  planes  are  parallel  to  the  axis. 
Hence,  the  perpendicular  thicknesses,  which  would  be  perpen- 
dicular to  the  several  tangent  planes,  at  the  point  of  contact  of 
each,  would  not  lie  in  the  same  plane ;  or,  conversely,  a  section 
on  any  helix,  KL,  or  radius  OI,  and  composed  of  perpendicular 
(normal)  thicknesses  at  all  points  of  either,  would  itself  be 
warped,  and  therefore  undevelopable. 

5°.  To  construct  radial  sections  of  a  blade. — Lay  off  on  the 
tangents,  as  at  n,  p,  g,  etc.,  the  vertical  thicknesses  at  those 
points,  viz.,  p'p',  Fig.  6,  at  g,  Fig.  2 ;  n'n',  at  nn,  etc.,  and  the 
shaded  figure,  nnpg,  will  be  the  radial  section  on  ng,  revolved 
into  the  paper. 

For  the  section  on  rE,  we  should  have  taken  the  thicknesses 
from  Fig.  6,  on  the  centre  line,  OO"O"'.  These  sections  are 
in  planes  containing  the  axis. 


MACHINE    CONSTRUCTION   AND   DRAWING.  235 

To  have  made  sections,  as  is  often  done,  perpendicular  to  the 
axis,  we  should  have  taken  K3T",  0'U",  etc.,  for  the  thicknesses. 
In  a  case  like  Fig.  5,  these  sections  are  taken  on  chords,  as  those 
of  C'"D'",  or  FG,  or  E"'H. 

The  figures  just  described  and  indicated,  should  be  con- 
structed in  full  on  a  much  larger  scale.  Let  the  radius  OE, 
Fig.  2,  for  example,  be  ten  feet,  and  let  that  and  the  figure  3, 
also  4,  and  5,  or  similar  ones,  be  made  on  a  scale  of  half  ax*,  inch 
to  one  foot. 

Ideas  Expressed  in  Modified  Forms  of  Screws. 

180.  Every  modification  of  the  screw  propeller,  from  the  form 
of   a  common  right  helicoid,  or   "true  screw,"  except  some 
merely  fanciful  or  arbitrary  ones,  has  been  the  result  of  a  cer- 
tain determining  idea,  suggested  or  confirmed  by  experiment  or 
reflection. 

181.  The  Idea  of  Axial  Expanding  Pitch. — In  this  case,  it 
being  known  that  a  screw,  beginning  to  work  in  smooth  water, 
soon  acts  to  move  rearward  a  column  of  water,  the  idea  is  that, 
as  the   entering  element   of    the   blade   moves   the   water  as 
described,  the  next  element  should,  so  to  speak,  chase  it  up,  so  as 
to  press  upon  the   moving   water  as   heavily   and   effectually 
as  the  first  element.     This  second  element  would  give  an  incre- 
ment of  velocity  to  the  already  moving  water,  and  so  the  third 
element,  by  a  continued  expansion  of  the  pitch,  would  move 
backward  faster  yet,  so  as  to  catch  up  with  the  water,  just  as 
men,  to  push  a  rail-car  with  a  uniform  pressure  as  its  speed  in- 
creases, must  walk  faster  and  faster. 

182.  The  idea  of  radially  expanding  pitch,  and  of  all  screws 
which,  by  having  a  curved  generatrix,  appear  bent  back,  that  is, 
from  the  vessel,  in  a  side  view  of  the  latter,  is,  to  counteract 
the  centrifugal  action  of  the  water,  and  confine  it  to  a  cylindri- 
cal column,  having  the  disc  (end  elevation)  of  the  screw  for  its 


Among  the  most  curious  screws  of  this  kind,  is  Holm's  con- 
choidal  screw,  having  a  rapidly  expanding  axial  pitch,  so  that  at 
the  trailing  edge  the  blade  is  tangent  to  a  plane  containing  the 
axis  of  the  screw,  and  therefore  has,  at  that  point,  an  infinite 
pitch.  Also,  at  the  outer  circumference  the  edge  of  the  blade 
is  bent  over  from  the  vessel  into  a  narrow  cylindrical  flange, 


236  ELEMENTS   OF 

which  finally  is  rounded  into  the  trailing  edge  at  the  corner,  by 
a  spherical  or  spoon-shaped  surface. 

183.  Finally,  the  opposite  idea  of  bending  the  blades  toward 
the  vessel,  and  of  mounting  them  on  rings,  so  as  to  leave  the 
central  portion  of  the  disc  open,  is,  to  favor  the  rush  of  water 
from  all  sides  into  the   partial  vacuum  which  tends  to  exist 
behind,  or  on  the  after  side  of  the  screw.    In  the  Griffith  screw, 
the  blades  are  widest  at  about  the  middle  of  their  length,  are 
bent  towards  the  vessel,  and  are  fitted  by  cylindrical  arms  into 
similar  sockets  in  a  large  spherical  hub,  or  " loss"     Each  can 
be  turned  on  the  axis  of  its  cylindrical  arm,  and  thus  the  pitch 
is  variable. 

If  a  screw  is  made  of  a  "  bent "  form,  as  seen  in  PI.  XXVII., 
Fig.  5,  merely  by  the  mo'vement  of  a  straight  generatrix,  which 
makes  a  constant  angle  of  less  than  90°  with  the  axis,  the  screw 
surface  is  simply  the  common  oblique  helicoid  (16-i),  or  that  of 
a  triangular  threaded  s.crew  (PL  III.,  Fig.  10). 

184.  While  preparing  these  pages,  I  am  informed  by  an  en- 
gineering friend  who  has  made  the  experiment,  that  if  saw  dust 
be  poured  upon  a  screw  model,  while  the  latter  revolves  rapidly 
in  a  lathe,  it  will  rather  be  drawn  towards  the  axis  of  the  screw 
than  dispersed  by  the  centrifugal  force,  developed  by  the  rotation. 

The  result  just  stated  may  be  explained  as  follows:  The 
rearward  discharge,  by  the  screw,  of  a  cylinder  of  water  creates 
a  constant  tendency  to  a  vacuum  at  the  position  of  the  screw. 
This  tendency,  being  constant,  is  as  effectual  as  a  sensible 
vacuum,  in  inducing  a  constant  rush  of  water  from  all  sides  to 
the  spot  where  the  screw  works.  This  centripetal  rush  of  water 
is  believed  to  prevail  over  its  centrifugal  tendency,  so  that  some, 
instead  of  bending  the  blades  aft,  or  from,  the  vessel,  to  confine 
the  water  radially,  and  so  prevent  its  lateral  dispersion,  and 
discharge  it  rearward  in  an  undiminished  cylinder,  have  bent 
them  forward  as  already  explained,  or  towards  the  vessel,  in 
order  to  favor  the  inward  rush  of  surrounding  water  at  the 
base  of  the  water  cylinder  acted  upon  by  the  screw.  The 
Griffith  screw,  as  said  before,  is  thus  formed. 

Historical  Note. 

185.  Sufficiently  patient  investigation  into    the  history  of 
every  perfected  mechanical  device  would  probably  show  that  it 


MACHINE   CONSTRUCTION   AND   DRAWING.  237 

had  its  origin  in  some  bodily  movement.  The  screw  propeller 
is  no  exception.  In  swimming,  the  hand  may  be  disposed, 
relatively  to  the  water,  somewhat  in  the  screw  form,  as  well  as  in 
that  of  a  flat  paddle  ;  and  when  intelligence  seeks  some  external 
aid  to  reinforce  and  extend  the  hand,  she  fashions  an  oar,  as 
used  in  sculling ;  where  it  is  constantly  submerged  and  is  vir- 
tually a  one-bladed  reciprocating  screw,  alternately  right- 
handed  and  left-handed  ;  while  oars  wrought  from  the  sides  of 
a  boat  in  the  'usual  manner  are  the  mechanical  rudiments  of 
paddle  wheels. 

186.  Robert  Hooke,  a  celebrated  English  mechanician  (1635 
— 1703)  believed  that  the  ancient  galleys  were  propelled  by  oars 
held  nearly  vertical,  always  submerged  and  subjected  to  a 
sculling  motion.  This  then  was  rudimentary  screw  propulsion, 
and,  reciprocally,  a  screw  propeller  is  a  "  continuous  sculling 
machine." 

Screw  propulsion  is  said  to  have  been  known  to  the  Chinese 
for  ages.  In  water,  it  is  but  the  companion  in  a  new  office,  of 
the  "  Archimedes'  Screw  "  for  raising  water,  and  the  counter- 
part of  the  immemorial  windmill  in  air. 

These  remarks  serve  to  show  how  shadowy  and  dimly  defined 
is  the  origin  of  the  invention  of  the  screw  propeller.  The  point 
selected  for  beginning  its  history  must  therefore 'be  somewhat 
arbitrary.  This  history  cannot  here  be  given.  Suffice  it  to 
say,  that,  beginning  with  Hooke,  Bourne  rehearses  about  two 
hundred  and  seventy-five  forms  or  modifications  of  inventions 
relating  to  propulsion  by  the  screw  or  by  analogous  devices. 

The  principle  of  axially  expanding  pitch  (176)  was  first 
patented  in  America,  and  applied  to  mill  water  wheels  by 
Clark  Wilson,  of  New  Hampshire,  in  1830.* 

It  had  been  patented  in  France  and  applied  to  propellers  in 
1824,  and  was  patented  in  England  in  1832. 

The  overhanging,  or  "  bent  back  "  form  was  first  patented  by 
Ebenezer  Beard  in  Connecticut,  in  1841,  and  in  England  by  the 
"  Earl  of  Dundonald,"  in  1843. 

Of  course  among  so  many  designers  as  have  been  indicated, 
many  reinvented  the  works  of  others,  many  merely  treated  de- 
tails and  accessory  features,  such  as  various  relations  of  the 
propeller  to  the  hull  of  the  vessel,  and  to  the  rudder ;  and 
means  for  raising  the  propeller.  Others  sought  to  produce  pro- 

*  Bourne,  p.  42. 


238  ELEMENTS    OF 

pellers,  which  should  be  adjustable  either  in  length  of  blade, 
or  in  the  inclination  of  the  surface  of  the  blade  to  the  axis,  by 
revolving  it  about  a  perpendicular  to  the  axis. 

Others,  emulous -of  ducks  and  fishes,  devised  fish-tail  and 
other  flexible  propellers  of  hinged  flaps,  or  of  steel  frames 
covered  with  gutta-percha,  which  should  adjust  themselves  to 
the  action  of  the  water.  Attempts  have  also  been  made  to  steer 
partly  or  wholly  by  screws,  either  by  having  two  independent 
screws,  one  on  each  side  of  the  stern,  which  could  be  revolved 
at  unequal  velocities,  or  by  deflecting  the  entire  screw,  in  case 
of  a  single  propeller,  so  that  it  might  revolve  in  any  plane 
oblique  to  the  shaft. 


EXAMPLE  LIU. 
The  Screw  of  the  "  Dunderberg." 

Description. — PL  XXYIIL,  Fig.  1,  represents  an  end  view 
of  two  blades,  as  seen  in  facing  the  stem  of  the  vessel,  and  an 
edge  view  of  the  hub,  two  blades  and  part  of  another.  This 
screw  is  "  bent  back"  15  inches.  The  direction  of  the  revolution 
being  as  shown  by  the  arrow  x,xf ;  ME' — M'E"  is  the  entering 
edge,  and  ND' — 2TD"  the  following  edge.  At  the  former  the 
pitch  is  27  feet.  On  RF'— ET"  it  is  28$  feet ;  and  at  ND'— 
N'D",  it  is  30  feet.  3' :  9"  =  45"  is  the  pitch  of  one  blade,  = 
one-eighth  of  the  total  extreme  pitch  of  30  feet,  and  WO"  is  its 
effective  length  ST. 

Thus  this  is  a  screw  of  axially  expanding  pitch,  bent  back,  by 
having  a  curved  generatrix  RT — R'T'. 

Construction. — This  is  pretty  nearly  evident  from  the  figure, 
by  the  letters  of  reference,  after  the  preceding  example.  Fig. 
2  shows  a  good  method  of  laying  out  the  cylindrical  blade  sec- 
tions (Ex.  LIT.  4°)  in  case  of  axial  expanding  pitch. 

DC,  for  example,  is  the  length  of  the  arc,  1 — 1,  of  the  end  view, 
MTN",  of  the  blade,  and  AD  is  the  pitch  of  the  blade,  then  AC 
is  the  development  of  the  helical  arc  1 — 1.  But  this  develop- 
ment is  curved ;  and  at  A,B,  and  C,  should  be  tangent  to  straight 
developments  of  helices  having  pitches  of  27,  28$  and  30  feet. 
Hence  make  AX  =  twice  the  pitch,  3' :  9",  of  one  blade  = 
7' :  6" ;  X#  —  yb  =  zc  —  twice  the  arc  1 — 1  of  the  end  view. 
&y  —  twice  the  pitch  of  one  blade  at  RT,  =  7'  :  2"  nearly ; 


MACHETE    CONSTRUCTION   AND   DRAWING. 


239 


and  As  =  twice  the  pitch  of  one  blade  at  NE'  —  6' :  9".  Then 
Aa,  Ab,  and  Ac  will  be  the  required  auxiliary  developments. 
The  curved  development,  AC,  is  now  drawn  so  as  to  be  tangent, 
at  A,  to  Aa ;  at  B,  to  a  line  parallel  to  Ab  ;  and  at  C,  to  a  line 
parallel  to  Ac,  as  required. 

The  dotted  figure  Am  Tn  is  an  example  of  the  conventional 
"development"  of  a  blade,  mentioned  in  (Ex.  L;  1°). 

187.  Referring  the  reader  again  to  works  on  propellers  alone, 
for  fuller  details,  the  subject  is  dismissed  with  the  following 
data  of  celebrated  examples,  from  which  the  student  can  con- 
struct additional  figures  for  himself. 

L  Sci'ew  of  the  U.  S.  N.  Steamer  ONEIDA. 
Diameter,  as  seen  in  end  elevation,  12'  :  9". 
Length,  parallel  to  the  axis,  22". 
Generatrix,  curved,  with  a  radius  of  15'  :  10£". 
Pitch,  expanding  axially,  from  18'  to  20'. 
Thickness  of  blades  at  the  hub,  5f ",  greatest. 

"          «       "         "       periphery,  f". 

Radial  section  of  greatest  thickness,  J-  of  the  width  of  blade 
from  the  entering  edge. 

Hub,  greatest  diameter,  22". 

"     bore  10£",  tapering  to  9£".  < fif 

No.  of  blades,  4 

2.  Screw  of  the  U.   S.  K  FRIGATE 
"  FRANKLIN." 
Diameter,  19'. 

Length,  41"  at  the  hub.     44"  at  peri- 
phery. 

Generatrix,  curved,  versed  sine  =  6" 
to  a  chord  of  19'. 

Pitch,    expands  axially  from  26'   to 
30'. 

Hub,  centre  diameter,  38",  Fig.  93. 
"     forward     «          30£". 
"     rear  "          26". 

"     (hollow)  internal  diameter,  20". 
"     length  of  body,  41". 
"     total  length,  83". 
Shaft  diameter,  S". 
Greatest  perpendicular  thickness  of  blade  at  hub, 


240  ELEMENTS   OF 

Greatest  perpendicular  thickness  of  blade  at  hub,  perpendicu- 
lar to  axis,  9f . 

Thickness  at  periphery,  f . 

Radial  sections,  or  templets,  in  planes  nearly  perpendicular  to 
the  axis,  that  is  taken  on,  or  parallel  to  the  chord,  as  E'"H, 
PI.  XXVIL,  Fig.  5,  of  the  generatrix,  and  perpendicular  to  the 
paper.  The  edges  of  these  templets  are  curved.  The  centre 
one  is  of  various  widths,  from  ll^-"  at  the  hub  to  T£"  at  the 
periphery  (Ex.  L;  5°), 


D— VOLUME  OPERATORS. 

EXAMPLE  LIY. 

Andrews' s  Centrifugal  Pump. 

Description.  Plate  XIII.,  Figs  6  and  7. — A  is  the  base  of  the 
pump,  cast  in  one  piece  with  the  case  C,  and  strengthened  by 
brackets  aa.  To  the  chamber  C,  by  flanges  W,  is  attached  the 
conducting-case,  composed  of  two  parts,  DD',  united  by  flanges 
dd',  forming  a  conic  spiral  discharge-passage,  g  and  E,  gradually 
enlarging  to  its  outlet.  F  is  the  stuffing-box,  through  which 
passes  the  cast-steel  driving-shaft.  G,  having  a  series  of  grooves 
turned  in  its  surface  at  J,  which  are  accurately  fitted  in  a  Babbitt- 
metal  box  in  the  standard  II,  and  its  cap  h,  counteracting  all 
tendency  to  end- thrust  or  vibration.  I  is  the  bed-plate,  having 
cast  upon  it  the  standard  II  and  brackets,  to  which  the  pump  is 
secured  by  the  flanges  dd'  and  base  A.  The  base  A  also  forms  a 
flange,  to  which  is  bolted  the  bend,  Q,  with  suction-pipe  B  attached 
(shown  broken  off),  with  a  foot-valve  (Fig.  96)  at  its  lower  end. 
To  a  flange  on  the  discharge-orifice, 
are  attached  pipes  for  conveying  the 
water  wherever  required. 

KK  is  the  disk  secured  upon  the  shaft 
G,  having' wings,  Fig.  94,  1,  2,  3,  4,  5,  6 
(see  Fig.  7),  upon  its  periphery,  closely 
fitting  the  space  between  it  and  chamber 
C,  within  which  they  revolve  without 
touching.  Their  discharge-ends,  ee,  ex- 
tend beyond  K,  close  to  case  I)',  without  touching  it,  and  ter- 


MACHINE   CONSTRUCTION   AND   DRAWING.  241 

minate  on  a  line  parallel  to  the  shaft  G.    -L  is  the  hub  cast  with 
and    connected    by    flanges   llll    (see   Fig.    95) 
to  chamber  C,  forming  spiral   introduction-pas- 
sages. 

In  the  end  of  the  shaft  G  is  a  steel  button,  n, 
with  a  convex  face,  which  revolves  in  contact  with 
the  convex  end  of  the  step  "N,  secured  in  the  hub 
L,  supporting  the  shaft  and  disk  when  run  verti- 
cally. Motion  is  communicated  to  the  disk  by  a 
belt  upon  the  pulley  P. 

Operation. — The  pump  and  pipes  first  being  filled  with 
water,  rapid  motion  is  given  to  the  disk  K,  when  the  centrifugal 
force  imparted  to  the  water  between  the 
wings  causes  it  to  flow  through  the  passages  g 
and  E,  to  the  outlet ;  a  vacuum  being  there- 
by created  between  the  wings,  causes  the 
water  to  rise  through  the  pipe  B,  to  keep  up 
the  supply. 

By  means  of  the  spiral  passages  around 
the  hub  L,  the  water  from  the  suction-pipe  is 
turned  gradually  from  a  direct  forward 
course  and  delivered  to  the  propelling  wings 
in  the  line  of  their  action ;  thence,  through  the  spiral  passages 
g  and  E,  it  is  again,  by  an  easy,  gradual  curve,  brought  back  to 
a  straight  course,  upon  reaching  the  outlet. 

The  wings  on  the  disk  K,  passing  beyond  its  outer  edge,  create 
and  maintain  a  vacuum  between  it  and  the  case  D,  and  prevent 
sand,  dirt,  etc.,  from  coming  into  contact  with  the  shaft.  The 
step  N  is  in  like  manner  protected  from  dirt,  enabling  the  pump 
constantly  to  discharge  a  large  proportion  of  sand,  gravel,  etc., 
without  injury  to  any  of  its  parts.  There  being  no  valves  in 
action  (the  foot  valve  remaining  open  while  the  pump  is  in 
motion,  and  used  only  to  retain  the  charge  when  at  rest),  and 
no  wearing  parts,  except  the  shaft  in  its  bearings,  which  is  per- 
fectly protected  from  dirt,  the  friction  is  reduced  to  the  small- 
est possible  fraction,  enabling  the  pump  to  run  for  years  with- 
out repairs. 

The  power,  lost  in  piston  pumps  in  overcoming  the  momen- 
tum and  inertia  of  the  water  at  each  stroke,  is  saved  by  this 
pump ;  also  the  large  amount  of  power  lost  in  changing  the  cur- 
rents of  water  at  right  and  other  angles — all  changes  of  direc- 
16 


242  ELEMENTS   OF 

tion  being  made  by  •  easy  gentle  curves — enabling  it  to  per- 
form the  same  work  with  much  less  power  and  a  greatly  de- 
creased velocity. 

Construction. — This  can  be  made  sufficiently  well,  since  these 
pumps  are  of  various  sizes,  by  taking  the  diameter  of  P=12", 
and  of  B=6",  for  a  scale. 

An  end  elevation  can  be  added,  by  making  the  vertical  plane 
of  the  outlet  flange,  tangent  to  the  flange  dd',  at  its  foremost 
point. 


MACHINE   CONSTRUCTION   AND   DRAWING.  243 


BOOK  SECOND. 

COMPOUND  ELEMENTS  OR  SUB-MACHINES. 

187.  As  soon  as,  by.  leaving  single  mechanical  organs,  we 
come  to  connected  series,  or  trains  of  pieces,  some  new  and  pe- 
culiar principles  relative  to  the  drawing  of  the  latter  are  re- 
quired. 

Not  only  the  form,  dimensions,  and  location  of  each  piece 
must' be  known,  but  the  character  of  its  motion,  must  be  under- 
stood also,  as  a  condition  for  knowing  the  nature  of  the  motion 
which  it  will  communicate  to  whatever  is  actuated  by  it.  From 
all  this  the  final  result  can  be  derived,  which  is  the  ability  to 
assign  to  each  piece  that  one  of  its  successive  positions  which 
corresponds  to  a  given  position  of  some  one  part,  taken  as  a 
standard,  to  which  the  others  are  referred. 

188.  Thus,  not  to  take  the  too  hackneyed  illustration  of  the 
crank  and  piston,  first  imagine  two  spur  wheels,  A  and  B,  in 
contact  at  T,  and  let  the  diameter  of  A  be  double  that  of  B, 
and  let  their  arms,  AT  and  BT,  be   on  the  line  of  centres. 
Then,  as  equal  lengths  of  arc  on  each  must  pass  the  point  T 
in  the  same  time,  a  revolution  of  45°  of  AT  will  produce  a  revo- 
lution of  90°  in  B. 


Fio.  97. 


189.  Again,  to  take  an  illustration  from  pulley  work,  Fig.  97. 

Let  A  be  a  fixed  point  or  pulley,  from  which  a  cord  proceeds 

to  the  movable  point,  B,  and  around  it  to  C.      By   drawing 


244  ELEMENTS   OF 

the  cord  till  B  moves  to  5,  we  shall  have,  by  reason  of  the  in- 
variable length  of  the  string  : 

AB  +  BC  =  A5  +  be,  or  by  decomposing, 

A.t>  -f-  £B  -f  B5  +  bC  =  A.b  +  bC  +  Cc,  in  which,  by  can- 
celling, Cc  =  2B5.  That  is,  if  the  free  end,  C,  of  the  cord  be 
moved  a  given  distance,  the  movable  point  will  move  half  as  far. 

In  the  second  case,  A  still  being  the  fixed  pulley,  but  the  cord 
being  fastened  to  the  movable  one,  B,  we  have  : 

BA  +  AB  +  BC  =  bA.  4-  A.b  +  be,  or,   by   decomposing, 

B5  +  &A  +  Ab  +  5B  +  B5  +  bC  =  bA  +  Ab  +  bC  +  Cc, 
from  which,  by  cancelling,  Cc  =  3B&. 

And  generally  the  place  of  a  movable  pulley  will  be  at  a  dis- 
tance from  its  initial  position  equal  to  one-nth  of  the  space  de- 
scribed by  the  free  end  of  the  cord,  where  n  the  number  of 
cords  at  the  movable  pulley. 

190.  As  most  examples  of  sub-machines  consist  of  fewer 
parts  than  any  whole  machines  possessing  much  interest,  it 
would  be  only  a  needless  anticipation  of  the  subsequent  ex- 
amples to  give  further  illustrations  here  of  the  general  idea 
which  should  be  constantly  in  mind  in  constructing  the  follow- 
ing examples,  which  is :  Where  is  each  piece,  and  what  is  its 
motion,  at  any  given  stage  of  the  motion  of  a  given  piece  ? 

ISTow,  when  the  given  piece  is  the  operator,  the  answer  to 
this  twofold  question  is  a  practical  invention,  consisting  of  a 
train  of  pieces  for  making  the  operator  accomplish  a  desired 
result. 

The  careful  study,  then,  of  the  following  examples,  with  con- 
stant attention  to  this  radical  idea,  and  to  the  kindred  question : 
How  else  could  the  same  result  have  been  accomplished?  is 
the  study  of  the  art  of  inventing,  so  far  as  that  is  an  acquirable 
or  teachable  one. 

From  the  foregoing  principles  it  may  be  seen  that  a  com- 
pound element  does  not  merely  consist  of  many  pieces,  having 
fixed  relative  positions,  and  acting  as  one  piece,  for  that  is  true 
of  cross-heads,  pillow-blocks,  pistons,  and  many  other  simple 
mechanical  organs.  But  a  compound  element  truly  consists  of 
several  moving  pieces,  each  of  which  moves  in  a  certain  way, 
according  to  the  motion  imparted  to  some  one  of  them. 


MACHINE   CONSTRUCTION   AND   DRAWING.  245 

SUPPORTERS. 

EXAMPLE  LY. 
A   Compound  Chuck. 

Description. — A  chuck  is  a  contrivance  attached  to  the  man- 
drel, or  supporting  axis  of  a  lathe,  for  the  purpose  of  holding 
the  work. 

Chucks  are  of  various  forms,  according  to  what  they  have  to 
hold,  and  the  work  to  be  done  upon  them,  whether  circular,  or 
other  turning,  external  or  internal ;  and  will  be  found  de- 
scribed in  any  of  the  accessible  popular  treatises  on  turning. 

Compound  chucks  are  of  three  principal  species  : — 

Scroll  Chucks,  Fig.  98,  where  the  spiral  tooth,  C,  acts  to  ad- 


vance or  retreat  the  jaws  A,  to  or  from  the  centre — 

Conical  or  wedging  Chucks,  which  separate  the  jaws  or  close 
them  together,  by  urging  them  into  a  conical  sheath  in  the  latter 
case,  or  withdrawing  them  in  the  former,  by  the  action  of  a 
screw ;  and — 

Geared  Chucks,  which  are  of  various  forms.  The  following 
figures  represent  Horton's  Geared  Screw  Chuck,  which  is  highly 
spoken  of  by  persons  engaged  in  the  finer  mechanical  pursuits 
of  making  small  and  exact  mechanism. 

Other  chucks  are  very  generally  modifications  or  combina- 
tions of  the  foregoing.  When  the  jaws,  D,  D,  D,  are  separately 
operated,  the  chuck  is  said  to  be  an  independent  jawed  chuck. 


24:6  ELEMENTS    OF 

Fig.  99  gives  a  view  of  this  Chuck  ready  for  use. 


I 


FIG.  100  represents  the  interior  of  the  back  plate,  with  the 
deep  groove  or  recess  containing  the  rack  G,  within  which  it  re- 


volves freely.  This  groove,  by  means  of  its  outer  and  inner 
flanges,  as  shown  by  figures  100  and  101,  forms  a  tight  casing 
for  the  gears,  thus  protecting  them  from  chips,  dust  or  any  mat- 
that  would  otherwise  injure  them. 

Fig.  101  represents  a  view  of  the  interior  of  the  front  plate 
showing  the  carrying  screws,  A  A  A,  and  the  nut  part,  N",  of  the 


MACHINE   CONSTRUCTION   AND   DRAWING. 


247 


jaws,  with  the  bevel  pinions  upon  the  former.   The  inner  ends  of 
these  screws  have  their  bearing  against  the  hub  L,  Fig.  100,  while 


the  shoulder  formed  by  the  pinion  near  the  outer  end,  rests  firmly 
against  the  outer  rim  of  the  groove,  in  which  the  rack  G  moves. 


Fig.  102  is  the  circular  rack,  seen  at  G,  Fig.  100. 

Fig.  103  gives  a  view  of  the  jaw,  which  is  forged  of  one  piece 
of  metal.  The  slots  for  the  jaws,  radiating  from  the  centre, 
leave  the  periphery  entire,  thus  securing  the  greatest  possible 
strength.  By  means  of  the  rack  and  geared  screws  in  this 
chuck,  great  facility  is  secured  for  moving  the  jaws,  so  as  to 
confine  any  article,  by  applying  the  wrench  to  any  one  of  the 
carrying  screws.  By  doing  this,  all  the  jaws  are  carried  forward 
at  the  same  time,  bringing  the  article  to  be  confined  at  once  to  a 
centre.  Then  when  wishing  to  confine  the  work  very  firmly,. 


248  ELEMENTS   OF 

pass  the  wrench  from  one  screw  to  the  other,  and  pull  upon  it 
sufficiently  to  take  up  the  back  lash  in  the  gearing.  By  con- 
tinuing this  operation,  one  can  fasten  the  work  tight  enough 
for  all  the  purposes  required.  The  jaws  to  this  chuck  can 
always  be  kept  very  accurate.  For,  by  means  of  the  gearing, 
they  may  at  any  time  be  adjusted  to  within  about  one-hundred 
and  fiftieth  pail  of  an  inch  of  a  true  circle.  They  can  also  be 
operated  independently,  by  simply  taking  the  rack  out  of  the 
back  plate,  thus  allowing  it  to  hold  any  kind  of  irregular  form 
of  work. 

The  jaws  are  case-hardened  with  animal  coal.  To  do  this 
thoroughly,  takes  a  number  of  hours,  and  is  apt  to  spring  the 
jaws.  To  obviate  this,  the  bite  of  jaws  is  ground  true 
after  the  chuck  is  finally  assembled  for  market,  which  makes  the 
jaws  as  true  as  they  were  left  after  first  turning. 

The  tightening  of  the  jaws 
by  "  taking  up  the  back-lash  " 

means  this.    When  a  pinion, 

A,  Fig.  104,  is  turned,  it 
draws  the  rack  R,  and  that, 
as  shown  at  K',  turns  the 

other  pinions.  The  back-lash,  which  is  the  difference  between  a 
tooth  and  a  space,  will  then  be  at  the  right  of  tooth  A,  and  at 
the  left  of  A'.  By  tiirning  A'  till  it  bears  upon  tooth  a',  the 
back-lash  will  be  said  to  be  taken  up.  It  may  be  more,  and 
then  the  back-lash  will  be  at  the  left  of  A.  Hence,  as  directed, 
all  the  pinions  should  be  turned  in  succession. 

Construction. — Figs.  99-103,  with  the  measurements,  which 
are  sufficiently  given,  may  serve  as  an  example  of  sketches  and 
measurements,  from  which  projections  can  be  drawn  with 
sufficient  accuracy  to  answer  every  purpose  of  a  graphical  exercise. 

191.  Other  compound  supporters,  are  compound  slide  rests, 
and  tool-holders. 

These  are  designed  to  give  one  or  more  motions  to  the  point 
of  the  cutting  tool  in  the  higher  power  lathes,  planers,  shaping, 
and  surfacing  machines. 

One  will  be  found  illustrated  in  connection  with  "  feed  mo- 
tions "  on  a  subsequent  page. 


MACHINE   CONSTRUCTION   AND   DRAWING.  249 


COMMUNICATORS. 

192.  Communicator 's,  are  perhaps  never  compound,  but  with 
the  small  space  left  at  our  disposal,  we  cannot  better  illustrate  the 
differences  (187-190)  between  the  drawing  of  detached  and  of 
connected  organs,  than  by  a  few  examples  of  groups  of  con- 
nected communicators. 

EXAMPLE  LYI. 
A  Beam,  Engine  Main  Movement. 

The  skeleton  figure,  PL  XXVIL,  Fig.  8,  answers  every  pur- 
pose of  a  finished  one,  so  far  as  to  show  how  to  find  the 
positions  of  other  parts  for  a  given  position  of  a  given  part. 

Let  the  vertical,  B</,  be  the  indefinite  axis  of  the  cylinder, 
and '  let  the  vertical,  Ho,  contain  a  diameter  of  the  crank  pin 
circle  JII".  This  diameter  is  equal  to  the  stroke  of  the  piston, 
and  so  are  the  vertical  chords  of  the  arcs  described  by  the  ends 
of  the  beam,  whose  centre  is  at  O.  Suppose  the  cylinder  end 
of  the  beam  to  be  connected  to  the  piston  rod  by  a  link,  B'J  / 
attached  at  5  to  a  cross  head.  Then  make  om  =  ge  =  BD,  the 
piston  stroke,  =  JH,  and  describe  the  arcs,  onm  and  gfe,  to  be 
described  by  the  ends  of  the  beam,  whose  length  will  then  be 
nf.  But  now  observe  that  appositions  of  the  ends  of  the  beam 
are  outside  of  the  verticals,  B</  and  Ho.  It  is  desirable,  how- 
ever, to  have  the  average  position  of  the  connecting  rod,  Him, 
vertical ;  and  so  of  the  link  B'5.  Hence  bisect  hf  at  C',  and 
nr  at  I',  and  draw  the  parallels  0J' — mil.' — etc.,  to  nf,  so  as  to 
make  the  new  vertical  chords  as  J'H'  equal  to  BD,  and  take 
OF  —  OC'  for  the  final  radius  of  the  beam  which  will  make  the 
mean  of  the  positions  of  the  connecting  rod,  and  of  the  link, 
vertical.  Draw  H'H,  the  lowest,  and  J'J  the  highest  position 
of  the  connecting  rod.  To  find  the  positions  of  the  crank  pin 
when  the  beam-end  is  at  I',  take  that  point  as  a  centre,  and 
IIH'  as  a  radius,  and  note  I  and  I",  where  the  arc  so  described 
cuts  the  crank  pin  circle.  Likewise  the  link,  being  of  constant 
length,  B'£  =  C'c  =  T)'d,  corresponding  to  the  lowest,  middle, 
and  highest  piston  rod  positions  B5,  Cc,  and  T)d. 

Finally,  to  find  the  position,  of  all  other  parts,  due  to  any 
given  piston  position  as  P. 


250 


ELEMENTS   OF 


1°. — Lay  off  vertically  from  P  the  constant  length  P^>  (not 
shown)  of  the  piston  rod. 

2°. — With^?  as  a  centre  and  the  constant  length  B'5,  of  the 
link,  as  a  radius,  describe  an  arc,  cutting  the  beam  arc,  D'C'B', 
in  the  required  position,  which  we  will  call  K,  of  the  right-hand 
beam-end.  Then  KO  to  K'  on  J'l'IT  will  be  the  beam  position. 

3°. — With  K/  as  a  centre,  and  H'H  as  a  radius,  describe  an 
arc  cutting  the  crank  pin  circle  in  a  point  Q,  which,  finally,  will 
be  the  required  crank  pin  position. 

EXAMPLE  LYII. 

"Wheeler's  Tumbling  Beam  Engine. 

A  skeleton  view  of  this  very  curious  form  of  steam  engine 
in  five  different  positions  of  the  crank,  etc.,  is  shown  on  PI. 
XXX.,  Figs.  4-8.  Here,  a,a  are  the  cylinders,  standing  on  the 
bed  plate  B.  C  is  the  crank  shaft,  which,  with  the  rocker 
shafts,  g,g,  works  in  fixed  bearings  in  a  common  frame.  "Rtt 
is  the  tumbling  beam,  no  point  of  which  is  fixed,  E,  being 
attached  to  the  crank-pin  R;  and  t  and  t  to  the  piston  rods.  It 
may  have  various  proportions,  but  an  isosceles  triangle,  whose 
altitude  BD,  Fig.  105,  is  equal  to  half  the  base  AC,  is  preferred. 


The  middle  point  B  (m,  PI.  XXX.)  moves  in  a  vertical  line,  it 


MACHINE   CONSTRUCTION  AND   DRAWING.  251 

being  also  the  middle  point  of  the  link  nn,  which  joins  the  free 
ends  of  the  equal  radius  rods,  K,K,  so  as  to  form  a  "parallel 
motion"  Iv,K  turn  on  the  centres  g,g.  P  and  Q  are  the 
pistons,  and  the  arrows  show  the  direction  of  their  motion,  at 
five  equidistant  positions,  45°  apart,  of  the  crank  pin. 

Starting  with  the  given  proportions  of  the  beams,  and  the 
facts,  that  when  one  piston,  a',  Fig.  105,  is  at  mid-stroke,  the 
other,  a,  is  at  the  end  of  its  stroke,  and  the  point  A,  Fig.  105, 
of  the  beam,  is  on  the  cylinder  axis  AJ',  we  can  determine  any 
other  pair  of  positions  ;  also  the  peculiar  property  of  this 
engine,  that  the  piston  stroke  is  greater  than  the  diameter  R<#, 
of  the  crank  pin  circle.  The  amount  of  this  excess  can  also 
be  found.  That  it  exists  is  obvious  on  mere  inspection  ;  for  if 
the  piston  positions  were  alike,  all  points  of  the  beam  would 
move  in  vertical  straight  lines  equal  to  the  diameter  IM.  But, 
by  reason  of  the  unlike  piston  positions,  the  beam  oscillates 
besides  ascending,  so  that  t  and  t,  and  thence  the  pistons,  must 
have  a  vertical  movement  greater  than  ~Rd. 

To  ascertain  the  relation  of  ns,  Fig.  105,  to  the  piston-stroke 
ac,  let  ACD  be  the  beam,  with  B  on  the  vertical  OB,  and  BA  = 
BC  =  BD,  and  D,  the  crank  pin  at  the  45°  point  from  n.  Thus 
BD  =  \  AC,  and 

De  =  Dt  =  $  CE  =  |  ac  (compare  Figs.  5  and  7.) 
But  OD  = 


or  2OD  =  ns  =       %  (ao)\ 

For  example,  let  ac  =  20",  then  ns,  or  the  throw  of  the  crank 
=  14.2  ;  and  the  length,  OD,  of  the  crank  =  7.1. 

The  points  tt,  see  the  Plate,  do  not  move  in  straight  lines,  but 
in  elongated  figure  8's.  Therefore,  in  the  absence  of  the  usual 
connecting  rods,  this  engine  belongs  to  the  variety  called  trunk 
engines,  in  which  the  piston  rod  is  a  hollow  cylinder,  called  the 
trunk,  and  links  join  the  points  t  with  the  piston,  and  pass 
through  the  trunk. 

193.  Other  novel  forms  of  steam  engine,  besides  rotary  ones, 
are  Roofs  Square  Engine,  consisting  of  a  rectangular  "  cylinder" 
and  two  rectangular  pistons,  one  within  the  other  and  moving 
on  the  two  centre  lines  of  a  rectangle,  while  the  inner  one  is 
attached  directly  to  the  crank  pin,  and  Hicks'  Engine;  both  of 
which  are  further  remarkable  for  compactness. 


252  ELEMENTS   OF 

EXAMPLE  LYIII. 
An  Eight-Day  Clock  Train. 

PL  XXXIII.,  Fig.  1,  shows  such  a  train.  The  circles  in  fine 
lines,  represent  the  pitch  circles  of  those  wheels,  which  especi- 
ally belong  to  the  hour  hand  movement. 

Each  wheel  is  designated,  1st,  by  its  radius ;  2d,  by  its  number 
of  teeth,  t;  3d,  by  the  time  of  one  revolution  of  it.  The  arrows 
indicate  the  directions  of  the  revolutions.  AB  is  the  pendulum, 
vibrating  once  in  each  second.  A.pp'  is  the  escapement,  oscil- 
lating in  unison  with  the  pendulum,  p  and  p'  are  its  pallets,  so 
adjusted  that,  as  the  pendulum  swings  to  the  left  of  its  vertical 
position,  tooth  a  of  the  scape  wheel,  passes  the  point  of  pallet  p, 
but  just  then  p'  catches  tooth  c  on  its  right  side,  so  that  the 
scape  wheel  moves  but  half  its  pitch  at  each  vibration  of  the 
pendulum.  Hence  a'  will  not  pass  j?,  till  the  pendulum  re- 
turns again  to  its  left  hand  position,  that  is,  in  two  seconds. 
Thus  the  scape  wheel,  having  30  teeth,  revolves  once  in  a 
minute,  and  may  carry  the  seconds  hand.  The  pitch  being 
made  the  same  for  all  the  wheels,  their  radii,  and  thence  their 
times  of  revolution  depend  on  their  numbers  of  teeth.  These 
are  clearly  expressed  on  the  figure.  Wheel  96£  is  on  the  end 
of  a  barrel  around  which  the  weight  cord  makes  sixteen  turns. 
It  can,  therefore,  make  16  revolutions  of  12  hours  each  before 
the  clock  will  run  down.  Wheels,  like  64#  and  40£,  which  revolve 
in  the  same  time,  may  be  on  the  same  physical  axis ;  but  wheel 
T2£,  which  carries  the  hour  hand,  is  on  a  hollow  axis,  through 
which  that  of  64£  and  40tf,  carrying  the  minute  hand,  passes. 

Other  Trains. 

194.  Let  us  now  examine  this  train  so  as  to  find  some  general 
relations,  variable  or  not,  between  the  train  and  the  final  results 
to  be  accomplished. 

1st.  Given  a  pendulum  vibrating  seconds,  which  is  conveni- 
ent ;  it  is  also  convenient  that  a  tooth  should  pass  a  pallet  only 
once  in  two  vibrations,  so  as  to  reduce  the  number  of  teeth  in 
the  scape  wheel.  Thirty  teeth  are  therefore  fixed  for  that 


MACHINE   CONSTRUCTION  AND   DRAWING.  253 

wheel  ;  and  one  minute  for  its  revolution.  The  action  of  wheel 
96£  being  more  conveniently  prolonged  by  making  many  turns 
of  the  cord  about  its  barrel,  than  by  making  that  wheel  with  96 
x  12  =  1152£,  in  order  to  revolve  it  once  in  eight  days,  we 
give  it  96  teeth  and  12  hours  =  720  minutes  for  a  revolution. 
That  done,  we  have 

-3-f^  as  the  velocity  ratio  desired,  between  wheels  96£ 
and  30t. 

Now  the  wheels  96#,  64£,  and  60t  are  successive  drivers,  and 
the  pinions  8t,  8t,  8t,  are  their  respective  followers,  and  re- 
volve in  the  same  times  as  the  wheels  on  the  same  axis,  and  we 
have 

96  x  64  x  60  720 


8x8x8 

"Whence  we  infer  that  the  velocity  ratio  of  the  extreme  axes 
of  a  train  is  equal  to  the  product  of  the  number  of  teeth  in  the 
drivers,  divided  by  that  of  the  numbers  in  the  followers,  which 

195.  To  show  by  a  converse  operation  how  simply  this  may 
be  seen  to  be  true,  let  the  ratio  -JLf-2-  be  given,  which  for  a  mo- 
ment we  will  take  as  the  ratio  of  a  wheel  of  720  teeth  working 
with  a  pinion  of  one  tooth,  though  this  would  practically  be 
impossible.  Now  decompose  the  terms  of  this  fraction  into  any 
factors  as  in  the  example, 

--  -  and  the  value  of  the  ratio  is  unchanged.     But, 
Ixlxl 

mechanically,  pinions  of  one  tooth  are  impossible,  while  arith- 
metically, a  fraction,  or  a  ratio,  is  not  changed  by  multiplying 

both  terms  by  the  same  number,  in  this  case  by  -  .  —  ,  giving 

J  J'S6 


96x64x60      ,.  ,  ,.    ,,  ,          .  ,      ,    .      ,, 

—  -  ,  which  are   practicable  numbers  of  teeth  for  the 
8x8x8 

wheels  and  pinions  of  the  train. 

Proceeding  in  this  manner,  as  the  numerator  may  be  variously 
decomposed,  we  may  have 

720    12x5x12    96x40x96     ,  , 

—  -  =  —  —  -  —  ——  —  •=  —  jr—  -z—,  where  the  numerators  of 
1         Ixlxl          8x8x8 

the  last  fraction  will  be  the  numbers  of  teeth  in  the  drivers,  and 


254 


ELEMENTS   OF 


train 


8  the  number  of  teeth  in  each  pinion  follower,  the  last  of  which 
carries  the  scape  wheel  on  its  axis. 

Again,  the  barrel  and  the  hour  hand  revolve  in  the   same 
time,  twelve  hours.     Accordingly  we  have  for  the  hour  hand 
96x40x6_12 
8x40x72    12* 

196.  These  trains,  and  other  similar  trains,  may  be  tabulated 
as  follows,  by  a  simple  system  of  notation  in  which  each 
wheel  is  expressed  by  its  number  of  teeth,  each  pinion  number 
is  written  under  the  number  of  that  wheel  which  drives  it ;  and 
those  of  wheels  on  the  same  physical  axis  are  written  on  the 
same  horizontal  line. 

We  have,  then,  the  following,  from,  which  the  student  can  con- 
struct the  drawings. 


I.— EIGHT-DAY  CLOCK. 


TRAIN. 

PERIODS. 

96  Barrel                   

1  h 

8                      61           10 

1  h 

8  60 
40  6 
8  30  

minute  hand. 
1  m. 

72               ... 

second  hand. 
12  h. 

hour  hand. 

IL— TWELVE-HOUR  CLOCK. 


TRAIX. 

PERIODS. 

IS  Earrd                                   OK                        * 

1  h 

6  30  scape 

Ini. 

25  min.  hand. 

Ih. 

48  h.  hand. 

12  h. 

MACHINE   CONSTRUCTION  AND   DRAWING.  25ft 

III.— EIGHT-DAY  CLOCK. 


1 

TRAIN. 

PERIODS. 

96  Barrel 

12  h 

g 

10                     10 

1  h 

8  96          | 

8  30  scape  
30                          10 

1m. 
3  h 

40.... 

12  h. 

,         „      ,     ,        ,       ,  ,     .     96x10x10   -12       ..    ,      ,, 
where  for  the  hour  hand  tram,  — — --- — — -  =  —  as  it  should. 

o  X  oO  X  40         iZ 

EIGHT-DAY  CLOCK. 


wl 

TRAIN. 

PERIODS. 

m 

m 

108  Barrel         

810m. 
90m. 

1m. 
Ih. 
12  h. 

12        108                          5 

1            1 

0 
3  hour  h. 

12—100 
10—30  scape. 
1 

6  min.  h. 
8 

iere,  for  the  hour  hand 

h    .    108x10      9      810m       810 

n  12x80       8        12  h        720 

197.  In  this  example  the  pinions  are  larger,  the  wheels  of  the 
pendulum  train  more  nearly  equal,  and  no  wheel  in  that  train 
(which  is  the  same  thing  as  the  escape- wheel  train)  revolves  in 
one  hour. 

When,  as  in  the  hour  hand  train,  the  extreme  axes  are  the 
same  geometrical  axes,  there  may  be  a  difficulty  in  adjusting  the 
radii,  if  the  pitch  is  the  same  as  in  the  escape-wheel  train.  It 
is  only  necessary  to  remember,  however,  that  the  velocity  ratios 
are  as  the  numbers,  not  the  sizes  of  the  teeth ;  and  only  those 
teeth  which  gear  into  each  other  need  have  the  same  pitch. 

198.  To  include  the  pendulum,  or  balance  wheel,  in  the  train, 
consider  that  as  a  tooth,  or  full  pitch,  of  the  escape  wheel  passes 


256 


ELEMENTS   OF 


a  pallet,  only  after  two  vibrations  of  the  pendulum,  if  e  be  the 
number  of  escape-wheel  teeth,  2  e  =  the  number  of  pendulum  vi- 
brations in  1  revolution  of  this  wheel.  And  if  the  pendulum 
makes  p  vibrations  per  minute,  then,  to  make  2  e  vibrations,  =  1 

revolution  of  the  escape  wheel,  will  take  —  minutes.      Then,  as 

the  hour  axis  revolves  in  1  hour,  =  60  m.,  the  ratio  of  the  revo- 
lutions of  that,  and  the  escape  wheel,  will  be 

60  -i-  —  =  60^     =  30-P 
p         2  e  e 

199.  If,  then,  a  watch  balance  vibrates  300  times  in  a  minute, 

i  "  *    *iD  /-,  rt          30  x  300       600 
and  the  escape  wheel  has  lo  teeth,  =,-(194)  =  — =— —  =  

and  if  there  be  three  axes  in  the  train,  each  with  a  pinion  of 

D       600  x93      81x72x75,     ... 

nine  teeth,  then     =-=  -— - — -r=— ~ —  — ^r--  will  express  the 
F        9x9x9        9x9x9 

train  from  the  hour  axis,  to  the  balance  wheel  axis  inclusive. 

Similarly,   a    month,   or   32-day   clock    may    be   designed. 
Lunar  and  annual  clocks  are  more  difficult.* 

Change  -  Wheels. 

200.  Analogous  principles  belong  to  change-wheels,  by  which 
any  given  velocity  ratio  is  given  to  two  axes  in  fixed  positions, 
as  in  a  lathe.     Thus,  let  the  required  set  of  velocity  ratios  be 
f»  £?  i>  i>  t>  £•     Since  the  axes  are  at  a  fixed  distance  apart, 
and  since  it  is  convenient  that  all  the  wheels  should  have  the 
same  pitch,  the  sums  of  their  numbers  of  teeth  must  be  con- 
stant, and  must  be  divisible  by  the  sum  of  the  terms  of  each 
ratio,  that  is,  in  this  example,  by  2,  3,  4,  5,  and  7.     The  number 
of  teeth  in  each  pair  is  therefore  the  least  common  multiple  of 
these  divisors  =2x2x3x5x7  =  420  and  the  teeth  in  the 
successive  pairs  will  be  as  follows : 


No.  OF  WHEEL  TEETH. 


210  —  210 
140  —  280 
105  —  315 
84  —  336 
168  —  252 
180  —  240 


See  Willis'  Prin.  of  Mechanism. 


MACHINE   CONSTRUCTION   AND   DRAWING.  257 

For  further  information  on  these  interesting  topics,  to  which 
only  an  introduction  can  here  be  given,  the  reader  must  consult 
the  larger  treatises  on  clock  and  mill- work. 

Example.— Let  the  ratios  be  |,  £,  •£,  f,  -§-. 


THE  SLIDE  "VALVE  AND  ITS  CONNECTIONS. 

•J101.  The  slide  valve,  and  its  connections,  may  be  considered 
among  the  foremost  of  sub-machines,  in  interest  and  importance ; 
on  account  of  the  high  office  whicli  it  fulfils,  in  the  working  of 
tne  grandest  of  motors  in  present  use,  the  steam  engine. 

The  office  of  the  valves  connected  with  any  steam  engine 
cylinder,  is  to  give  the  steam  access  to  each  side  of  the  piston, 
alternately,  and,  at  the  same  time,  to  provide  an  escape  for  the 
steam  which  ha&  just  been  effecting  a  piston  stroke. 

202.  Valve  moilons  in  general  are  classified  as 

1.  Cock  valves. 

2.  Poppet  valves,  see  Ex.  XLIV. 

3.  Slide  valves.     Ex.  XLII. 

Slide  valves  ate  the  ones  most  used,  and  are  those  which 
most  invite  investigation.  They,  with  their  connections,  may 
be  classified  as 

1.  Yalve  motions  with  one  valve, 

2.  "  "          "     two  valves, 

each  of  which  is  subdivided,  according  to  the  most  important 
ground  of  distinction,  into 

1.  Motions  with  invariable  cut-off. 

2.  «  "     variable       "    " 

203.  We  will  now  suppose  the  student  never  to  have  exam- 
ined the  subject  at  all,  further  than  by  simple  inspection  of 
engines  in  motion,  or  partly  dissected  for  repair ;    and  will 
therefore  begin  with  a  rudimentary  example,  in  which  only  the 
radical  features,  without  the  various  adjustments  of    refined 
practice,  will  be  noted.     See  PL  XXIX.,  Fig.  1. 


General  Description  of  Parts. 

204.  B  is  a  fragment  of  the  bed  plate  (Ex.  XVI.)  or  general' 
support  of  the  engine.     P  is  the  steam  piston,  see  PL  IV.;:  Fig,. 
IT 


I>03  ELEMENTS   OF 

1,  and  (Exs.  XX.  and  XXI.)  which  is  urged  backward  and  for- 
ward, in  a  rectilinear  path,  by  the  pressiire  of  steam,  acting  on 
its  opposite  faces  alternately. 

M  is  a  section  of  the  main  shaft  or  crank  shaft,  which  is 
made  to  revolve  in  fixed  bearings  (Exs.  I.,  II.,  and  III.)  by  a 
suitable  connection  with  the  piston. 

CC  is  the  steam  cylinder,  within  which  the  steam  is  confined, 
so  as  to  take  effect  upon  the  piston.  H  is  the  front,  and  h, 
partly  broken  out,  the  back  cylinder  head.  Both  are  bolted  to 
the  ends  of  the  cylinder.  See  Ex.  X. 

P'  is  the  piston  rod,  which  passes  through  a  stuffing  box,  not 
shown,  in  the  back  head  h,  and  is  firmly  attached  to  the  cross- 
head  O,  which  moves  in  fixed  guides — not  shown — and  parallel 
with  the  piston  rod.  See  Ex.  VIII. 

R  is  the  connecting  rod,  partly  broken  to  show  other  parts, 
and  jointed  at  o  to  the  cross-head  and  at  the  other  end  to  the 
crank  pin  Q,  by  a  joint  like  Ex.  XXVI. 

N  is  the  crank,  keyed,  as  at  &,  to  the  shaft,  M.  Supposing, 
then,  that  motion  is  already  established  in  the  direction  of  the 
arrow,  the  motion  of  the  piston  P,  from  its  present  extreme  right 
position  to  its  extreme  left  position,  will  turn  the  crank  from 
the  +  90°  point  to  —  90°,  through  F.  This  motion  of  the  piston, 
from  m  to  n,  is  called  its  stroke.  The  return  stroke  turns  the 
crank  and  shaft  from  —90°  to  +90°,  through  D.  The  com- 
plete result  is  expressed  by  saying  that  one  double  stroke  of  the 
piston  produces  one  revolution  of  the  shaft,  or  an  angular 
motion  of  360.° 

205.  When,  as  is  sometimes  done,  the  crank  shaft  M,  is  not 
also  the  main  shaft,  but  is  connected  with  the  latter  by  gearing, 
the  double  stroke  of  the  piston  might  produce  more  or  less  than 
one  revolution  of  the  main  shaft. 

Pile  driving  engines,  where  the  piston  speed  is  usually  very 
great,  are  examples  of  the  latter  case,  and  some  propeller 
engines,  of  the  former.  Since  the  piston  has  no  tendency  to 
move  the  crank,  when  the  latter  is  in  the  positions  MQ  or  MQ', 
the  points  Q  and  Q'  are  called  dead  points;  also,  centres. 

206.  How  now  does  the  steam  gain  access  to  the  opposite 
sides  of  the  piston  alternately? 

An  eccentric,  see  Ex.  XXIX.,  being  suitably  mounted  on  the 
crank  shaft  M,  the  eccentric  rod,  partly  shown  at  X,  where  the 
connecting  rod  R  is  broken  away,  is  jointed  at  d  to  the  foot  of 


MACHINE    CONSTRUCTION   AND   DRAWING.  259 

the  hanging  rocker  arm  a.  This  arm,  and  its  counterpart,  the 
standing  rocfar  A,  oscillate  together  on  the  roc/c  shaft,  r,  to 
which  both  are  keyed.  A  is  jointed  at  e  to  the  valve  stem,  L. 
The  latter  carries  the  yoke,  yy,  which  embraces  the  steam  valve 
Y.  This  valve  is  hollow,  as  at  I,  like  an  uncovered  box  turned 
upside  down.  See  also  Fig.  2. 

T  is  the  steam  chest,  into  which  "  live  steam  "  enters  from  the 
boiler,  by  the  steam  pipe,  terminating  at  S.  Its  walls  and 
bottom  are  solid  with  the  cylinder  C.  Its  cover  is  bolted  on. 

s  and  s'  are  the  steam  passages,  leading  from  the  steam  chest 
to  the  opposite  ends  of  the  cylinder.  In  the  direction  of  the 
circumference  of  the  cylinder,  or  as  seen  on  an  end  view,  these 
passages  extend  about  one-third  around  the  cylinder. 

E  is  the  exhaust,  and  opens  through  the  chimney  or  smoke- 
stack into  the  atmosphere ;  or,  in  condensing  engines,  into  the 
condenser,  Exs.  XI.  and  XII.  p  and  p'  are  the  steam  ports, 
and  u  is  the  exhaust  port.  These  are  three  long  and  narrow 
parallel  rectangular  openings  in  the  valve  seat,fg,  on  which  the 
valve  moves,  bb,  the  partitions  between  the  steam  and  the  ex- 
haust ports  are  the  bridges. 

The  valve,  Y,  is  so  proportioned  to  the  ports,  and  is  so  moved 
that  but  one  steam  passage  at  a  time  can  be  open  into  the 
steam  chest,  and  but  one  steam  port  together  with  the  exhaust 
port  can  be  covered  at  once  by  the  hollow  interior,  I,  of  the 
valve.  It  is  by  such  an  arrangement  as  this,  that  steam  is 
admitted  to  the  opposite  ends  of  the  cylinder  alternately. 

207.  Let  us  nest  look  at  the  action  of  the  parts. 

General  Action. 

As  a  rudimentary  example,  sufficient  to  illustrate  the  general 
action  of  the  slide  valve,  let  the  valve  be  adapted  to  the  parts 
as  shown  in  PI.  XXIX.,  Fig.  1.  At  its  extreme  right  position, 
let  the  port  p,  be  wholly  open  to  the  interior  I ;  at  its  extreme 
left  position,  let  the  same  port  be  wholly  open  to  the  steam  chest. 
It  is,  therefore,  now  just  at  mid-stroke,  moving  left,  and  ready  to 
open  the  port^?.  As  it  opens  this  port,  steam  enters  and  pushes 
the  piston  to  the  left  to  the  mid-stroke  position  GK,  when  the 
p;>rt,  _p,  will  be  wide  open,  the  valve  at  the  extreme  left,  and 
ready  to  return.  When  the  piston  has  reached  the  extreme 
left,  at  nn,  the  valve  will  be  at  mid-travel  again,  but  moving  to 


260  ELEMENTS   OF 

the  right,  and  ready  to  open  the  port  p  for  the  return  piston 
stroke. 

While  the  valve  is  opening  and  closing  the  steam  port,  p,  to 
the  steam  chest,  it  is  simultaneously  opening  and  closing  the 
port  p'  to  the  exhaust  passage  E,  through  the  interior  chamber 
I.  Thus  the  steam  used  in  the  preceding  stroke  from  n  to  ra, 
escapes  into  the  atmosphere,  through  s' ,  the  port  p',  and  E. 

208.  Such,  then,  as  to  its  main  features,  is  the  composition 
and  action  of  a  slide  valve  motion.     What  are  the  modifying 
causes  of  subordinate  variations  in  this  action? 

The  line  from  the  shaft  centre  to  the  crank  pin  centre, 
properly  represents  the  crank,  and  may  be  called  the  crank  arm. 
The  line  from  the  shaft  centre  to  the  eccentric  centre,  is  like- 
wise the  eccentric  arm,  and  is  the  linear  crank  which  is  equiva- 
lent to  the  eccentric.  Twice  the  length  of  the  latter  line  is,  in 
simple  valve  motion,  exactly  equal,  and  in  valve  motions  gene- 
rally, as  in  link  motions,  approximately  equal  to  the  travel,  that 
is,  the  stroke,  of  the  valve.  Finally,  the  acting  surfaces  w  of 
the  valve  may  just  cover  the  ports,  or  may  overlap  them  on  one 
or  on  l)oth  sides  of  each  port  p  and  p' . 

209.  Three  things,  then,  \st,  the  angle  between  the  crank 
and  the  eccentric  arms ;    2<#,  the  length  of   the  latter    arm, 
called  also  the  eccentricity,  and  3d,  the  relative  sizes  and  posi- 
tion of  the  valve  faces,  and  the  valve  ports,  materially  affect 
the  particulars  of  the  distribution  of  the  steam  to  the  steam 
cylinder  and  from,  it  to  outer  spaces,  as  we  shall  now  pro- 
ceed to  show,  taking  them  up  from  the  point  of  view  of  desi- 
rable results  to  be  produced. 

Modifications  and  Adjustments. 

210.  The  preceding  rudimentary  account  up  to  (208)  neglects 
the  following  particulars. 

1°.  The  influence  of  the  connection  of  the  reciprocating 
motion  of  the  cross  head,  with  the  rotary  motion  of  the  crank 
pin. 

2°.  The  advantage  of  employing  the  steam  expansively,  by 
cutting  off  its  admission  before  the  completion  qf  each  stroke, 
so  that  the  simple  elasticity  of  the  confined  steam  should  effect 
the  completion  of  the  stroke.  The  point  in  the  stroke  at  which 
admission  of  steam  ceases  is  called  the  cut  off. 


MACHINE   CONSTRUCTION   AND   DRAWING.  261 

3°.  The  importance  of  using  the  steam  itself,  in  place  of  com- 
plications of  balancing  mechanism,  even  if  such  were  possible, 
to  gradually  overcome  the  inertia  of  the  heavy  reciprocating 
parts  and  so  avoid  damaging  shocks  at  the  points  of  changing 
the  direction  of  the  piston  stroke.  This  is  partly  accomplished 
by  closing  the  exhaust  before  the  end  of  the  stroke.  The  period 
during  which  the  exhaust  thus  remains  closed  is  called  the  com- 
pression. 

4°.  The  release  of  the  steam  behind  the  piston,  a  little  before 
the  completion  of  a  stroke,  so  that  it  may  have  time  to  escape 
in  part  before  the  beginning  of  a  new  stroke. 

5°.  The  convenience  and  elegance  of  likewise  employing  the 
steam  itself  to  neutralize  the  results  of  certain  minor  and  almost 
necessary  imperfections  in  workmanship.  This,  with  a  further 
accomplishment  of  the  third  object  (3°)  is  secured  by  admitting 
steam  for  a  given  stroke  just  before  the  completion  of  the  pre- 
ceding stroke.  The  opening  of  the  steam  port  at  the  beginning 
of  the  stroke  is  called  the  lead  of  the  valve. 

Definitions. 

211.  In  connection  with  these  proposed  results,  and  available 
means  for  producing  them,  the  following  definitions  arise ;  which 
are  here  presented,  together,  for  convenience  of  future  reference, 
though  some  of  them  may  have  been  given  already. 

1st.  The  distance  from  one  extreme  position  of  any  given 
point  of  the  valve  to  the  other  like  position  of  the  same  point  is 
the  travel  or  stroke  of  the  valve.  The  centre  line,  yy,  of  the 
valve,  PI.  XXIX.,  Fig.  3,  is  a  convenient  line  to  represent  the 
valve  for  the  purpose  of  marking  its  travel. 

2d.  The  excess  outward,  as  Z,  Fig.  4,  by  which  the  valve  face 
extends  outward,  beyond  its  steam  port,  when  the  valve  is  at 
midstroke,  is  the  outside  lap  of  the  valve,  commonly  called 
simply  the  lap. 

3d.  If,  as  in  Fig.  4,  the  valve  being  there  at  midstroke,  its 
interior  chamber  were  limited  as  at  the  inner  dotted  lines  ;  the 
small  space =i,  would  be  the  inside  lap. 

4th.  The  amount  of  opening  of  the  steam  port  at  the  begin- 
ning of  a  stroke  is  the  outside  lead  of  the  valve  commonly 
called  its  lead.  That  is,  lead  admits  steam  to  the  piston  before 
the  latter  "begins  a  stroke. 


.262  ELEMENTS   OF 

5th.  The  amount  of  opening  of  the  exhaust  passage,  at p'  for 
instance,  if  the  piston  is  moving  from  C  to  A,  Fig.  4,  when  the 
piston  has  reached  A,  is  the  inside  lead.  That  is,  inside  lead 
allows  steam  to  escape  before  the  end  of  a  stroke  is  reached. 

6th.  The  point  at  which  admission  of  steam  ceases  is  the  cut- 
off. This  term  is  also  applied  to  the  separate  valve  often  used, 
by  which  the  cutting  off  is  effected. 

7th.  From  the  point  of  cutting  off,  to  the  opening  of  the  ex- 
haust passage,  is  \hz  period  of  expansion,  as  the  one  from  where 
the  steam  port  begins  to  open,  to  the  time  of  cut-off,  is  the 
period  of  admission. 

8th.  From  the  time  the  exhaust  passage  closes  till  it  is  re- 
opened for  admission  is  the  period  of  compression. 

Exhaust  naturally  and  mainly  takes  place  before  the  piston, 
but  inside  lead  opens  an  exhaust  passage  behind  the  piston, 
before  the  latter  has  finished  its  stroke. 

9th.  The  point  at  which  the  exhaust  opens  is  the  release  /  and 
is,  as  said,  the  close  of  the  period  of  expansion. 

10th.  If,  as  in  Fig.  4,  the  length  oo'  of  the  interior  of  the 
valve  is  greater  than  the  exhaust  port  +  the  two  bridges,  the  ex- 
cess, as  o,  on  eacli  side,  is  called  the  clearance. 

llth.  The  difference  between  90°  and  the  angle  made  by  the 
eccentric  arm  with  the  crank,  is  the  angular  advance  of  the 
eccentric. 

12th.  The  arc  or  angle  of  the  eccentric  arm  motion,  which 
would  move  the  valve  through  a  space  equal  to  a  given  lap,  and 
so  as  to  just  close  a  steam  port  by  that  motion,  is  called  the  lap 
angle. 

13th.  The  angular  distance  of  the  crank-pin  from  Q,  when 
the  steam  port  begins  to  open,  is  the  lead  angle.  An  equal 
angular  motion  of  the  eccentric  is  its  lead  angle. 

212.  Taking  up  the  above  topics  (210)  in  the  order  named, 
the  connection  between  the  cross-head,  O,  and  crank-pin,  Q, 
may  be  indirect,  through  the  medium  of  the  connecting  rod,  R, 
or  direct  as  in  PL  XXIX.,  Fig.  3,  where  the  outer  extremity  of 
the  piston  rod  is  expanded  vertically  into  a  slotted  yoke  ;  which  is 
simply  the  mechanical  equivalent  of  a  connecting  rod  of  infinite 
length ;  or  of  a  line,  perpendicular  to  the  piston  rod,  and 
always  containing  the  centre  of  the  crank-pin,  and  therefore 
equal  to  the  diameter  of  the  crank-pin  circle.  In  this  form  of 
connection,  the  motions  of  the  piston,  piston  rod,  yoke,  and 


MACHINE   CONSTRUCTION   AND   DRAWING.  263 

crank-pin,  in  the  direction  of  the  axis  of  the  cylinder,  are 
simultaneous  and  equal. 

The  ends  of  the  rocker  arms  might,  likewise,  move  in  small 
slotted  yokes,  attached  to  the  valve  stem,  and  eccentric  rod ; 
but  by  balancing  their  arcs  as  in  PL  XXVII.,  Fig.  8,  or 
PI.  XXIX.,  Fig.  3,  no  sensible  irregularity  will  appear  in  their 
small  motion. 

THEOREM  XXII. 

In  either  mode  of  connection,  the  velocity  of  the  crank-pin 
is  uniform  /  and  that  of  the  piston  is  variable. 

It  is  important,  in  order  to  avoid  injurious  shocks,  especially 
in  heavy  machinery,  that  its  parts  should  move  with  uniform 
velocity.  But  all  the  machines  of  a  given  assemblage  derive 
their  motion  ultimately  from  the  main  shaft  of  the  prime  mover, 
through  one  or  more  lines  of  shafting,  from  which  belts  or  gear- 
ing pass  to  the  separate  machines,  and  which  revolve  uni- 
formly. Hence  the  main  shaft  should  likewise  revolve  uni- 
formly. 

The  rest  of  this  preliminary  and  general  theorem  may  now 
be  sufficiently  demonstrated  from  PL  XXIX.,  Fig.  1. 

Let  the  crank-pin  circle  be  divided  into  eight  equal  parts,  to 
represent  eight  equidistant  positions  in  the  uniform  rotary 
motion  of  the  crank-pin.  Then  take  the  constant  length,  Qo, 
of  the  connecting  rod,  in  one  pair  of  dividers,  and  the  constant 
length,  #P,  of  the  piston  rod  in  another.  Then  from  1,  2,  3, 
etc.,  on  the  crank-pin  circle,  as  centres,  describe  arcs,  with  Qo, 
as  a  radius,  and  from  their  successive  intersections,  temporarily 
noted,  with  the  centre  line  MP,  lay  off  the  distance  oP  ;  which 
will  give  the  piston  positions  1,  2,  3,  etc.,  corresponding  to 
the  equidistant  crank-pin  positions  above  described ;  as  is  evi- 
dent from  the  nature  of  the  connection  of  the  moving  parts. 
Now,  because  the  successive  equal  arcs  0°-1 ;  1-2 ;  etc.,  are 
more  and  more  nearly  parallel  to  the  line  of  direction  Mp  of 
the  piston  motion  the  nearer  they  are  to  U,  it  follows  that  the 
corresponding  successive  advances  of  the  piston  from  P,  to  3,  2, 
etc.,  must  be  at  first  greater  and  greater ;  while  as  the  craiik- 
pin  approaches  the  point,  Q',  they  must  be  less  and  less,  as  at  2'- 
3',  and  3V.  And  it  also  follows  that  this  result  must  be  true, 
in  general,  for  both  the  described  forms  of  connection. 


264  ELEMENTS    OF 


THEOREM  XXIII. 

The  piston  positions,  corresponding  to  crank  pin  positions 
which  are  equidistant  from  the  same  dead-point,  are  identical 
for  either  connection  separately, 

This  very  evidently  results  in  the  direct  connection,  PI. 
XXIX.,  Fig.  3,  from  the  fact  that  the  yoke,  de,  is  constantly 
perpendicular  to  the  piston  rod,  and  moves  with  it  as  one  piece  ; 
so  that  the  piston,  for  example,  will  be  at  f,  whether  the  crank 
pin  be  at/"7  or/"",  these  points  being  equidistant  from  the  same 
dead-point,  a  (205). 

The  same  result  follows  in  the  indirect  connection,  from  the 
constant  lengths  of  the  crank  and  the  connecting-rod,  so  that, 
for  example  in  PL  XXIX.,  Fig.  1,  triangles,  as  oJ'M  and 
0J"M,  are  always  equal,  and  have  the  side  oM  common,  the 
points  J'  and  3"  being  equidistant  from  Q. 

213.  The  movement  of  the. piston  from  m  to  n,  being  its 
stroke,  the  same,  together  with  the  return  from  n  to  m,  is  called 
a  double  stroke,  and  evidently  corresponds  with  a  complete  re- 
volution of  the  crank  pin,  beginning  at  Q. 

Let  the  crank  pin  motion  UQW,  be  called  the  front  half 
of  its  motion,  and  WQ'U  its  back  or  rear  half,  and  let  the  two 
divisions  of  the  double  stroke  corresponding  to  these  semicircles 
be  called  the  front  and  hack  segments  of  the  double  stroke. 

The  piston  motion  is  thus  properly  referred  to  the  crank-pin 
motion  as  a  standard,  because  the  latter  is  uniform,  Theor. 
XXII.  And  the  crank-pin  circle  is  divided  thus  by  the 
diameter  LTW,  instead  of  by  any  other  diameter,  because, 
Theor.  XXIII.,  the  piston  positions  in  either  connection  are  the 
same  for  crank-pin  positions  equidistant  from  the  opposite  ex- 
tremities of  UW. 

THEOKEM  XXIY. 

The  segments  of  the  double  stroke  are  equal  in  the  direct 
connection,  and  the  front  one  is  the  greater  in  the  indirect  con- 
nection. Conversely,  etc. 

This  proposition  is  sufficiently  obvious  from  mere  inspection 
of  PI.  XXIX.,  Fig.  3,  in  case  of  the  slotted  yoke  connection, 


MACHINE   CONSTRUCTION  AND   DRAWING.  265 

since  the  motions  of  the  piston,  yoke,  and  crank-pin,  are  all 
equal  in  the  direction  of  the  piston  motion.  Thus,  when  the 
piston  has  advanced  from  A  to  B,  the  yoke  has  advanced  from 
a  to  de,  carrying  the  crank-pin  an  equal  horizontal  distance, 
ao,  from  a  to  d.  That  is,  the  half  semicircle,  ad,  of  the  crank- 
pin  motion,  corresponds  with  the  half-stroke,  AB,  of  the  piston. 

Again,  in  Fig.  1,  operating  as  in  Theor.  XXII.,  we  find 
G'K'  to  the  left  of  the  centre  line,  GJ,  as  the  piston  position 
corresponding  to  the  crank-pin  positions,  U  or  W,  which  estab- 
lishes the  first  part  of  the  theorem. 

Conversely,  the  segments  of  the  crank-pin  circle,  correspond- 
ing to  the  equal  segments  of  the  double-stroke  each  side  of 
GJ,  are  unequal  in  the  crank  connection,  the  forward  one  being 
the  less.  To  show  this,  we  have  only  to  take  the  length,  0Q, 
of  the  connecting-rod,  as  a  radius,  and  o',  the  position  of  o  at 
mid-stroke,  GJ,  of  the  piston,  as  a  centre,  and  describe  the  arc 
FMD,  through  M,  since  M#'=Q0  or  o'o=T£m  or  Kw-y  and  D 
and  F  will  be  the  crank-pin  position,  corresponding  to  the  mid- 
stroke  position  of  the  piston. 

Natural  Zero  Points  of  the  Piston  and  Crank-pin  Motions, 
and  Segments  of  the  Double-Stroke. 

214.  At  first  glance  it  seems  natural  to  divide  the  double- 
stroke  into  its  two  single  strokes,  as  its  most  simple  component 
parts,  and  to  place  the  zero  points  at  Q  and  Q',  PI.  XXIX., 
Fig.  1. 

But,  as  we  have  seen,  the  two  segments  of  the  single-stroke 
which  correspond  to  two  successive  quadrants  of  the  crank-pin 
circle,  reckoned  from  Q  to  Q',  are  unequal ;  and  the  piston 
positions,  corresponding  to  equal  arcs  each  side  of  MU,  are  un- 
symmetrical  with  GJ.  And,  besides  this,  in  the  earlier 
segment  of  the  stroke  are  the  lead  and  admission,  and  in  its 
later  one  are  the  cut-off  and  compression  and  release.  That  is, 
the  two  segments  of  the  single  stroke  are  unlike,  both  in  their 
piston-positions,  and  their  characteristic  events. 

On  the  other  hand,  if  we  take  the  zero  point  of  the  piston 
motion  at  the  position  corresponding  to  the  position  of  the 
crank-pin  on  MU,  we  shall  have  food,  admission,  cut-off,  com- 
pression and  release  on  each  side  of  G'K',  corresponding  to  the 
crank-pin  motions,  UQW,  and  UQ'W. 


266  ELEMENTS    OF 

Again,  as  the  crank-pin  motion  is  uniform-,  let  its  path  be 
the  one  to  be  divided  into  equal  segments  by  its  zero  points,  and 
let  the  irregular  divisions  be  on  the  stroke,  where  the  motion^ 
also,  is  variable,  and  where  the  events  of  the  two  parts  of 
each  stroke  are  dissimilar. 

We  will  therefore  take  U  as  the  zero  point  of  the  crank-pin 
circle,  and  reckon  180°  each  way  from  it.  Then  let  G'K',  the 
corresponding  piston  position,  be  the  zero  point  of  the  piston 
motion,  and  let  the  distances  from  G«K',  each  way  to  the  end 
of  the  stroke  and  back,  be  the  segments  of  the  double  stroke. 

The  steam  cylinder  may  thus  be  regarded  as  a  compound 
one,  composed  of  two  cylinders  of  unequal  length,  estimated  in 
opposite  directions  from  the  section  G'K',  as  a  common  base, 
in  the  common  initial,  or  zero  plane  of  both. 

Distinguishing  the  pistons  of  the  two  forms  of  connection  as 
the  crank  piston  and  the  yoke  piston,  we  have  the  following 
theorem. 

THEOREM  XXV. 

The  crank  piston  is  ahead  of  the  yoke  piston  during  the 
stroke  towards  the  shaft,  and  behind  it  during  the  opposite  stroke. 

Since  the  segments  mK  and  nK  of  the  double-stroke,  PI. 
XXIX.,  Fig.  1,  are  equal  in  the  yoke  connection,  the  accelera- 
tions of  the  piston  from  m  to  K  are  exactly  symmetrical  with 
those  from  n  to  K,  that  is  also  with  the  retardations  from  K 
to  n. 

Since  the  like  segments,  PO  and  n'O,  are  unequal  in  the 
crank  connection,  PO  being  the  greater,  while  both  are  tra- 
versed in  the  same  time,  the  acceleration  from  P  to  0  is  more 
rapid  than  from  n'  to  0,  that  is,  than  the  retardation  from  0 
ton'. 

Hence  it  follows  that  as  the  pistons  of  each  connection  start 
together,  from  the  position  Pra,  the  crank  piston  will  gain  on 
the  yoke  piston  till  the  former  is  at  K'G' ;  the  latter  being  at 
the  same  time  at  G-K.  Then  the  yoke  piston  will  gain  on  the 
crank  piston  till  both  coincide  at  nn. 

Therefore  the  crank  piston  is  ahead  of  the  yoke  piston  during 
the  stroke  towards  the  shaft,  and  conversely,  as  is  sufficiently 
evident,  is  behind  the  yoke  piston  during  the  stroke  from  the 
shaft. 


MACHINE   CONSTRUCTION  AND   DRAWING.  267 

But  it  is  still  to  be  noted,  that  after  the  crank  piston  has 
gained,  till  it  is  ahead  by  the  space  from  GK  to  G'K',  the  yoke 
piston  makes  up  this  loss  and  catches  the  former  at  nn.  Then 
starting  together  at  nn,  the  yoke  piston  gains  during  the  back 
semicircle  of  the  crank  pin,  till  ahead  by  the  same  space  it  lost 
before,  when  the  crank  piston  makes  up  its  loss  and  catches 
the  yoke  piston  at  P.  Thus  the  division  of  the  double  stroke 
adopted  in  (214)  is  further  justified. 

Cut  Off. 

215.  Let  that  part,  v,  of  the  valve,  which  covers  a  steam  port, 
be  called  its  lip  /  and  when  the  lip  is  of  the  same  width  as  the 
steam  port,  and  when  the  eccentric  centre,  as  in  the  foregoing 
examples,  is  just  90°  behind  the  crank  pin,  let  the  arrangement 
be  called  a  radical  valve  motion;  it  being  the  one  from  which, 
as  a  base,  to  proceed  to  make  all  necessary  modifications.  The 
eccentric  centre  will  be  thus  situated  because  the  valve  is  at 
mid-stroke  when  the  piston  is  at  the  end  of  its  stroke  ;  exactly 
so  in  PL  XXIX.,  Fig.  3,  and  sensibly  so  in  Fig.  1,  owing  to  the 
length  of  the  eccentric  rod,  as  compared  with  the  eccentric  arm. 

The  main  events  in  the  valve,  or  piston,  stroke  are  the  point 
of  admission  of  steam  to  produce  a  stroke  ;  the  point  of  cut- 
ting off ;  the  moment  of  closing  the  exhaust,  by  which  steam 
is  pent  up  before  the  piston  ;  and  the  moment  of  release,  when 
the  steam  which  is  producing  a  given  stroke  begins  to  escape. 

It  will  now  be  convenient  to  study  the  separate  effects  of 
angular  advance,  and  of  lap  (211)  upon  these  events. 

THEOREM  XXYI. 

The  effect  of  a  given  angular  advance  of  the  eccentric,  witt 
be  to  afford  "  admission "  for  a  new  stroke,  "  cut-off"  "  ex- 
haust closure "  and  "  release"  all  at  an  equal  number  of  de- 
grees before  reaching  a  dead  point. 

Let  the  crank  pin  be  at  any  position  as  +45  PL  XXIX. ;  Fig. 
3,  and  moving  towards  a.  The  eccentric  centre  will  then  be 
90°  behind  it,  at  h.  Let  h  now  be  revolved  22£°  to  L  Then 
hbk  is  the  angular  advance.  Then  when,  in  the  revolution  of 
the  main  shaft,  Jc  has  come  to  the  diameter,  ed,  the  crank  pin 
will  be  at  +  67£°,  that  is  22|°  from  the  next  dead  point  a. 


268  ELEMENTS   OF 

But  when  ~k  comes  to  ed  the  valve  will  be  at  mid-stroke,  and 
moving  towards  the  shaft,  and  hence  admission  at  n  begins  for 
the  next  stroke  ;  cut  off  at  n'  takes  place  for  the  present  stroke, 
the  piston  being  at  k',  found  by  making  k'h'  =  B5  =  a  A ; 
and  exhaust  closure  and  release  occur  simultaneously  at  t  and 
t',  respectively,  at  the  same  time  with  the  other  events. 


THEOREM  XXYII. 

of  a  given  lap,  alone,  corresponding  to  a  certain 
number  of  degrees  from  tfie  zero  diameter,  is,  to  postpone  ad- 
mission for  an  equal  number  of  degrees  beyond  the  dead  point ; 
to  produce  cut-off  at  the  same  number  of  degrees  before  the 
dead  point ;  with  release  and  exhaust  closure  at  the  dead  point. 

This  theorem  is  best  established  by  considering  the  valve  as  at 
mid-travel,  PL  XXIX.,  Fig.  4,  where,  to  avoid  confusing  Fig. 
3,  the  cylinder  and  valve  are  considered  as  simply  translated  to 
the  left,  with  the  valve  placed  at  midstroke,  and  lengthened  by 
the  lap,  I,  at  each  end.  When  the  valve  is  at  mid-travel,  and 
moving  backward,  its  slotted  yoke  is  on  de,  Fig.  3,  and  the 
piston  at  A  is  ready  for  a  stroke  to  the  left.  The  piston  rod, 
issuing,  as  before,  at  C,  is  supposed  to  be  connected  with  its 
yoke  de  by  links  from  a  long  cross  head,  and  passing  along 
each  side  of  the  engine. 

Remembering  that  the  valve  and  its  yoke  move  in  opposite 
directions,  with  a  rocker  arm,  I  must  be  laid  off  to  the  right  of 
de,  on  ba,  to  give  the  yoke  position,  mm',  corresponding  to  the 
beginning  of  admission,  at^>,  when  the  crank-pin  will  be  at  N, 
so  that  N5ra  shall  be  90°. 

Thus  N  is  as  many  degrees  beyond  a,  as  m  is  beyond  de.  The 
angle  mbd  is  called  the  lap  angle. 

Again,  cut-off,  on  the  stroke  from  C  to  A,  evidently  took  place 
at^/,  when^/  was  just  closed  by  the  valve,  moving  to  the  left. 
Then  mm'  was  as  far  to  the  left  of  de,  and  N  as  far  above  a, 
as  the  same  points  now  are  beyond  de  and  a,  in  the  direction 
of  rotation,  S.  Exhaust  closure  occurred  at  mid-stroke  of  the 
valve,  and,  there  being  no  angular  advance,  this  would  be  at  the 
dead  point  of  the  piston.  Release,  also,  only  begins  when  the 
valve  has  reached  mid-stroke,  which  is  at  the  end  of  the  piston 
stroke,  that  is  at  a  dead  point. 


MACHINE    CONSTRUCTION    AND   DRAWING.  269 

It  is  thus  evident  that  no  very  serious  evil  results  from  lap 
alone  except  to  postpone  admission  beyond  the  moment  of  be- 
ginning a  stroke. 

To  avoid  this  effect,  angular  advance  and  lap  must  be  com- 
bined, observing  that,  separately,  they  have  opposite  effects 
upon  the  time  of  beginning  admission.  Let  us  next  examine 
their  joint  effect,  as  illustrated  in  a  problem. 


PROBLEM  XXY. 

To  produce  a  cut-off  at  a  given  crank-pin  position,  witliout 
preventing  proper  admission,  etc. 

Let  it  be  required,  PL  XXIX.,  Fig.  5,  to  cut  off  at  a  crank- 
pin  position  of  50°  ;  where  ac,  the  stroke  diameter,  =  AC  the 
stroke,  where  dg  is  the  yoke,  and  G  the  piston  position  at  cut- 
off, Gg  being  =  BB'  =A#. 

B'A,  perpendicular  to  the  crank  arm,  BW,  will  be  the  position 
of  the  eccentric  arm,  for  the  radical  valve  having  neither  angu- 
lar advance  nor  lap.  The  port,  j?',  is  therefore  open  by  the 
space  h'b'  — A5,  and,  as  the  two  last  theorems  show,  it  cannot 
be  closed  at  the  present  piston  position,  by  angular  advance 
alone,  or  lap  alone,  without  displacement  of  the  other  main 
events  of  the  stroke.  Now,  if  we  advance  the  excentric  arm 
B'A  to  B'&,  20°,  or  half  way  to  the  mid-stroke  position,  the 
opening  Ti'V  will  be  partially  closed  by  the  amount  h'c'=hc,  and, 
with  the  same  valve,  admission,  by  Theor.  XXYI.,  would  occur 
20°  too  soon.  If,  then  we  complete  the  closure  by  a  lap,  Vc'  = 
be,  corresponding  to  the  lap  angle  nB'fc  of  20°,  the  cut-off  will 
be  effected  at  the  desired  point ;  and  admission,  which  would 
be  20°  too  late,  by  Theor.  XXVIL,  with  lap  alone,  is  hastened 
by  the  equal  contrary  effect  of  the  angular  advance. 

Hence  to  produce  cut-off  at  a  given  crank-pin  position,  set 
the  pin  at  that  position,  give  an  angular  advance  to  the  excen- 
tric equal  to  one-half  the  difference  ad  between  the  Crank-pin 
position  and  90°,  and  add  to  the  outer  edges  of  the  valve  a 
lap  =  to  the  perpendicular  distance  from  the  new  excentric 
position  to  the  mid-stroke  diameter, 


270  ELEMENTS    OF 


PROBLEM  XXYL 

To  determine  the  exhaust  closure  and  release,  for  the  ad- 
justed cut-off  and  admission. 

As  the  addition  of  lap,  that  is  outside  lap,  to  the  valve  does 
not  at  all  affect  the  positions  of  the  inner  edges  of  the  valve, 
relative  either  to  each  other  or  to  the  edges  of  the  ports,  we  have 
only  to  consider  the  effect  of  angular  advance,  alone,  upon  the 
times  of  exhaust  closure  and  the  opening  for  release,  just  as  in 
the  case  of  a  valve  without  lap. 

But,  by  Theor.  XXYL,  the  effect  of  a  given  number  of  de- 
grees of  angular  advance  is,  to  fix  the  occurrence  of  all  the  main 
events  of  the  stroke  at  an  equal  number  of  degrees  before  reach- 
ing a  dead  point.  Hence,  for  a  valve  giving  a  certain  point  of 
cut-off,  the  exhaust  closure  at  p.  Fig.  3,  and  the  opening  for  re- 
lease at  j?',  which  are  simultaneous,  take  place  at  a  crank  position 
as  far  from  a  (90°)  as  there  are  degrees  of  angular  advance. 


THEOREM  XXYIII. 

The  travel  of  a  valve  with  lap  is  the  sum  of  twice  the  lap 
added  to  twice  tlw  steam-port  opening. 

To  establish  this  clearly,  refer  to  PL  XXIX.,  Fig.  4,  where 
the  valve  is  at  mid-stroke.  The  total  travel  evidently  consists 
of  the  sum  of  the  distances  traversed  to  the  right  and  the  left  of 
the  mid-position. 

First,  then,  at  the  port,  p',  the  valve  must  first  travel  to  the 
right,  by  a  space  =  I,  the  lap,  before  the  port  will  begin  to  be 
opened,  and  then  further  in  the  same  direction  until  the  port^?' 
is  opened  to  the  extent  required. 

Second,  the  like  successive  movements  must  take  place  from 
the  mid-position  to  the  extreme  left  in  order  to  first  begin,  and 
then  continue  the  opening  of  the  port  j9,  equally  with  p' . 

The  entire  movements  from  mid-stroke  are  thus  equal ;  each 
is  thus  the  semi-travel,  and  their  sum  is  the  travel  of  the 
valve ;  which  is  sensibly  equal  (208)  to  the  throw  of  the  eccen- 
tri-c,  that  is  to  the  diameter  of  the  circle  described  by  the  cen- 
tre of  the  eccentric. 


MACHINE    CONSTRUCTION   AND   DRAWING.  271 


THEOREM  XXIX. 

Inside  lap  prolongs  the  expansion  and  hastens  compression  ; 
while  inside  clearance  hastens  the  release  and  postpones  the 
beginning  of  compression. 

In  PI.  XXIX.,  Fig.  5,  the  valve  fl'KRF,  whose  interior  length 
is  II,  has  neither  inside  lap  or  clearance,  H  being  equal  to  oo' ' , 
If  the  piston,  G,  be  moving  in  the  direction  of  arrow  P,  the 
valve  will  be  moving  as  at  P',  the  crank  pin  and  eccentric  cen- 
tres being  at  d  and  k,  and  cut-off  is  just  occurring  at  I',  and 
expansion  beginning.  If,  then,  the  length  of  the  interior  open- 
ing were  less  than  II,  in  which  case  there  would  be  inside  lap, 
it  is  clear  that  the  port,  p,  would  be  closed  sooner  than  it  will 
be  now,  which  would  cause  compression,  before  the  piston,  that 
is  between  G  and  A,  as  the  piston  is  now  moving,  to  begin  sooner 
than  it  now  will. 

At  the  same  time,  p'  would  evidently  be  opened  later  than  it 
will  be  now,  which  will  prolong  the  time  of  expansion,  and 
postpone  the  release,  which  takes  place  behind  the  piston. 

On  the  other  hand,  if  II  were  greater  than  it  it  now  is,  there 
would  be  inside  clearance,  and  p  would  evidently  be  closed  later 
than  it  will  be  now  ;  and  the  compression  would  be  postponed 
and  shortened.  At  the  same  time,  p'  would  be  opened  sooner 
than  it  will  be  now,  and  thereby  expansion  would  be  abridged 
and  release  hastened. 

To  repeat,  and  summarily :  When  there  is  neither  inside  lap 
nor  clearance,  the  opening  of  one  port  and  the  closing  of  the 
opposite  one  by  the  inner  edges  of  the  valve,  are  simultaneous 
and  dependent  on  the  angular  advance  alone  (Theor.  XXVL). 
Inside  lap  hastens  the  closure  of  the  port  before  the  piston,  and 
thereby  hastens  compression  •  and  retards  the  opening  of  the 
port  behind'the  piston,  and  thereby  prolongs  expansion  by  post- 
poning the  release. 

Inside  clearance  has  just  the  opposite  effects; 

Continuing  the  summary,  but  relative  to  the  outer  valve  edges 
for  convenience  of  reference,  we  have,  from  Theor.  XXYIL, 

Outside  lap  postpones  admission  and  hastens  cut-off  ;  but 
has,  of  itself,  no  effect  on  exhaust  closure  or  release. 

Angular  advance  hastens  admission,  cut-off,  exhaust  closure, 
and  release. 


272  ELEMENTS    OF 

Outside  clearance,  if  ever  there  were  such  a  thing,  would 
have  just  the  opposite  effect  from  outside  lap.  Thus,  if  the 
extreme  length  of  the  valve,  Y,  PI.  XXIX.,  Fig.  1,  were  less 
than  the  sum  of  the  bridges  and  the  three  ports,  both  ports 
would  be  partly  open  at  once  at  mid-stroke  ;  steam  would  have 
access  to  both  sides  of  the  piston  at  once,  and  cut-off  of  the 
stroke  from  ri  to  P  would  not  take  place  till  P  had  proceeded 
some  distance  from  P  to  n'  on  the  next  stroke. 


PROBLEM  XXYII. 

To  determine  tJie  effect  of  the  eccentric  upon  the  valve  motion, 
and  to  counteract  it,  in  part. 

To  illustrate  the  nature  of  this  effect,  it  will  be  sufficient  to 
refer  to  PI.  XXIX.,  Fig.  1. 

When  the  piston  is  at  P,  if  the  valve,  Y,  is  at  mid-stroke,  as 
it  should  be,  the  eccentric  centre  will  be  in  a  position  analogous 
to  D,  found  by  taking  d  as  a  centre,  when  de  is  vertical,  and 
dM.  as  a  radius,  and  describing  an  arc  which  will  cut  the  circle 
made  by  the  eccentric  centre,  in  the  corresponding  position  of 
that  centre ;  above  QQ',  for  the  motion  represented  by  the 
arrows.  The  motion  of  the  eccentric  and  valve  is  thus,  though 
on  a  smaller  scale,  a  counterpart  of  that  of  the  piston  and  crank ; 
but  the  irregularity  is  relatively  smaller,  owing  to  the  much 
greater  length  of  the  eccentric  rod  as  compared  with  the 
eccentric  arm,  than  is  found  in  the  ratio  of  the  connecting  rod 
t6  the  crank. 

Also,  through  the  intervention  of  the  rocker,  the  smaller  seg- 
ment of  the  double  stroke  of  the  valve  is  its  forward  one.  That 
is,  the  common  base,  analogous  to  G'K',  of  the  two  segments  is 
to  the  right  of  G  J. 

To  Tceep  the  valve  at  mid-stroke,  as  at  Y,  Fig.  1,  while  the 
eccentric  centre  is  90°  back  of  the  crank  pin,  as  on  U"W,  we 
have  only  to  lengthen  the  eccentric  rod.  It  will  then  follow  that 
the  shorter  segment  of  the  double  stroke  of  the  valve  will  be  to 
the  right  of  GJ,  and  therefore  the  width  of  port  opening  at  p' 
will  slightly  exceed  that  at  p.  That  is,  the  port  p  may  not  be 
fully  opened,  or  the  port  p'  may  be  overpassed,  or  more  than 
opened. 


MACHINE    CONSTRUCTION    AND    DRAWING.  273 

Distribution  of  Power. 

216.  As  the  motion  of  the  crank  pin  is  uniform,  while  the 
average  load  carried  by  the  engine  is  supposed  to  be  uniform 
also,  the  power  applied,  while  the  crank  pin  is  traversing  the 
semicircle  UQW,  should  be  equal  to  that  applied  to  it  on  the 
semicircle  WQ'U.     A  perfect  engine  therefore  would  seem  to 
be  one  in  which  the  power  exerted  in  the  sub-cylinder,  K'G'P, 
while  the  piston  should  pass  from  K'G'  to  P  and  back,  should 
equal  that  expended  in  the  smaller  sub-cylinder,  IL'G'n. 

Whether  this  could  be  practicably  and  advantageously  accom- 
plished by  making  the  valve  faces  and  steam  ports  unsymmetri- 
cal  with  GJ,  so  as  to  cut  off  nearer  to  n',  on  the  stroke  n'P,  than 
to  P,  on  Pfl/,  is  a  question  which  may  be  left  to  mechanical  en- 
gineers and  designers,  and  to  the  larger  treatises  on  valve  motions. 

The  limits  of  this  volume  only  permit  the  question  to  be 
raised,  whether,  as  just  implied,  it  would  be  possible  to  make 
the  work  in  K'G'P,  that  is  the  average  pressure  on  the  piston 
when  passing  from  q  to  P  and  back,  multiplied  by  the  distance 
2qP,  equal  to  the  work  in  K'G'n'  =  the  average  pressure  when 
going  from  q  to  n'  and  back  x  2  qnf. 

Just  this  may  be  noticed :  With  a  constant  effort  applied  to 
to  the  crank  pin  tangentially  to  its  circle,  a  less  total  effort 
will  be  required  on  the  arc  DQF,  and  hence  a  less  average 
pressure  on  the  piston,  from  GK  to  P  and  back,  than  from  GK 
to  n'  and  back ;  and  as  the  eccentric  motion  makes  the  cut-off 
occur  later  on  the  stroke  from  P  to  nf,  owing  to  the  greater  irre- 
gularity of  the  piston  motion,  Theor.  XX V.,  this  diminished 
pressure  can  be  obtained  by  the  earlier  cut-off  on  the  stroke 
from  in!  to  P. 

Lead. 

217.  Owing  to  wear  of  the  bearings  of  the  crank,  and  the 
cross  head  pins,  and  the  necessity  in  some  cases  of  a  minute 
play  of  these  pins  in  their  bearings,  to  avoid  too  much  stiffness 
and  binding,  the  sum  of  QO  and  OP,  PI.  XXIX.,  Fig.  1,  is  not 
precisely  constant,  in  actual  mechanism.     During  the  stroke 
from,  the  shaft,  that  is  from  n  to  m,  Q  and  o  are  at  their 
greatest  distance  apart,  being  pulled  apart  by  the  steam,  acting 
on  the  left  side  of  P.     During  the  opposite  stroke,  Q  and  o  are 
pushed  together.     The  change  takes  place  at  the  ends  of  a. 

18 


274:  ELEMENTS    OF 

stroke,  and  if  not  made  gradually,  by  slowly  overcoming  the 
momentum  of  the  moving  parts,  the  result  is  an  injurious,  and, 
to  the  ear,  disagreeable  "  thumping,"  or  "  pounding,"  upon  the 
centres.  Now  compression  tends  to  overcome  this  momentum, 
but  if  employed  to  the  very  extremity  of  the  stroke,  or  a  hair 
beyond,  it  injures  the  admission  for  the  succeeding  stroke. 
Instead,  therefore,  of  relying  only  on  the  compression  of  the 
confined  steam  of  the  previous  stroke,  it  is  better  to  also  admit 
the  "  live  steam "  for  the  next  stroke,  an  instant  before  the 
beginning  of  that  stroke.  The  opening  of  the  port  at  the  point 
of  beginning  a  stroke  is  called  the  lead  of  the  valve.  The  cor- 
responding distance  of  the  crank  pin  from  a  dead  point,  is  called 
the  lead  angle  (212).  The  lead  angle  may  vary  from  0°  to  8°. 

PROBLEM    XXVIII. 

To  provide  a  certain  lead  angle  without  disturbance  of  the 
cut-off. 

By  Theor.  XXVI.,  angular  advance  hastens  both  admission 
and  cut  off. 

Outside  lap  retards  admission  and  hastens  cut  off.  Hence 
a  reduction  of  it  hastens  admission,  and  retards  cut  off. 

If,  then,  we  increase  the  angular  advance  of  the  valve,  say 
3°,  from  k,  PI.  XXIX  ;  Fig.  6,  the  valve  will  begin  to  open  the 
port,  p,  3°  before  the  crank  pin  reaches  the  -f-  90°  point,  and 
the  cut  off  will  also  occur  3°  sooner  than  now,  or  at  47°. 

But  if  we  also  reduce  the  lap  by  an  amount  corresponding 
to  3°  from  &,  the  cut-off  point  will  retreat  3°,  from  47°  to  50° 
again,  and  the  admission  will  be  further  hastened  from  3°  to 
6°  in  all.  That  is,  admission  will  begin  when  the  crank  pin  is 
6°  from  the .+  90°  point. 

Hence  to  produce  a  given  lead  angle,  as  required,  increase 
the  angular  advance  by  half  that  angle,  and  reduce  the  lap  by 
the  other  half. 

PROBLEM  XXIX. 

To  determine  the  effect  of  lead  on  exhaust  closure,  release, 
and  travel. 

Since,  by  Prob.  XXVI.,  exhaust  closure  and  release,when  there 


MACHINE   CONSTRUCTION   AND   DRAWING.  275 

is  neither  inside  lap  nor  clearance,  depend  only  on  angular  ad- 
vance, which  hastens  both,  the  increase  of  this  advance  by  3° 
hastens  the  both  of  the  events  named  by  the  same  amount. 

The  total  angular  advance  being  now  23°,  the  exhaust  closure 
and  release  will  take  place  at  the  +  67°  position  of  the  crank 
pin,  instead  of  at  the  +  70°  position  as  before. 

Finally,  as  the  semi-travel  equals  the  sum  of  the  port  open- 
ing and  the  lap,  the  reduction  of  the  lap,  made  to  procure  lead 
without  altering  the  cut  off,  has  reduced  the  total  travel  by  twice 
this  reduction  of  lap. 


THEOREM  XXX. 

The  Angulw  Advance,  estimated  from  the  zero  radius 
hitherto  taken,  is  equal  to  the  sum,  of  the  lap  and  lead  angles-, 
estimated  from  the  same  point. 

See  PL  XXIX.,  Fig.  6,  giving  an  enlarged  view  of  the  quad- 
rant n  B'M  of  figure  5.  B'M  is  the  semi-travel.  Here,  when 
the  angular  advance  is  increased  from  .hk  (=  Jcri)  to  hr,  by 
half  the  lead  angle,  the  new  lap  =  the  space  L. 

Now,  reckoning  from  n,  we  have  ns  —  hr,  by  making  ks  = 
kr,  as  T&r  is  at  once  the  increase  of  the  angular  advance,  and 
the  decrease  of  the  lap  angle,  n  B'&,  by  half  the  lead  angle. 
Thus  ns  =  the  angular  advance,  =  the  angular  measure  of  the 
sum  of  the  lap  L,  and  the  lead  I,  also  estimated  from  B'n. 


THEOREM  XXXI. 

When  the  steam  port  is  open  by  the  amount  of  the  lead, 
the  opposite  port  is  open  for  exhaust  ly  the  amount  of  the  lap 
and  lead. 

See  PI.  XXIX.,  Fig.  4,  where  the  valve  is  at  mid-stroke,  and 
supposed  to  be  moving  left.  Before  the  steam  port  p,  for  the 
time,  can  open  at  all,  the  lap  I  must  be  overcome,  and  then  the 
exhaust  port  p'  will  be  open  to  an  equal  extent. 

Again,  when  the  steam  port  p  is  opened  to  a  certain  amount 
of  lead,  the  exhaust  port,^',  will  be  evidently  opened  further, 
by  the  same  amount,  which  makes  its  total  opening  as  enunci- 
ated. 


276  ELEMENTS   OF 


Port  Opening. 

218.  In  many  engines,  the  steam  ports  are  alternately  used 
for  the  admission  and  the  exhaust  of  steam.  Various  considera- 
tions bear  upon  their  proportions. 

First.  Steam,  during  admission,  maintains  a  nearly  uniform 
pressure,  while  during  the  exhaust  a  single  cylinder  f  \\\\  of  steam 
forces  itself  into  the  atmosphere  by  its  own  elasticity,  and  with 
diminishing  velocity  as  its  tension  decreases  by  expansion.  Hence 
when  separate  ports  are  used  both  for  admission  and  exhaust, 
the  latter  should  be  the  larger,  and  when  one  port  serves  both 
purposes,  it  should  be  adjusted,  as  to  size,  so  as  to  secure  a  free 
exhaust. 

Second.  The  speed  of  the  piston  evidently  affects  the  areas 
of  the  steam  and  exhaust  ports,  both  in  relation  to  each  other, 
and  to  the  piston  area.  When  the  piston  speed  is  great,  so  that 
the  piston  follows  up  the  escaping  steam  so  rapidly  as  to  partly 
push  it  out  of  the  cylinder,  the  average  tension  of  the  escaping 
steam  will  differ  less  from  that  of  the  incoming  steam,  than  in 
case  of  slow  piston  speed  ;  and  the  steam  and  exhaust  ports  may 
be  more  nearly  equal.  Thus,  it  is  stated,  that  for  piston  speeds 
not  greater  than  200  ft.  per  minute,  the  area  of  the  exhaust 
may  well  be  0.04  of  that  of  the  piston,  and  that  of  the  steam 
port  0.02^  of  the  same ;  while  for  a  piston  speed  of  600  ft.  per 
minute,  the  exhaust  port  area  should  be  0.10  of  that  of  the 
piston  and  that  of  steam  port  0.08  of  the  same.  In  the  latter 
case  both  ports  are  larger,  and  also  more  nearly  equal. 

Third.  When,  as  in  most  cases,  one  port  serves  for  both 
admission  and  exhaust,  the  size  and  travel  of  the  valve,  and  the 
positions  of  the  ports,  should  be  so  adjusted,  that  the  valve  will 
open  the  ports  fully  for  exhaust •,  and  partially,  to  the  due  pro- 
portionate extent,  for  admission. 

This,  of  course,  cannot  be  done  with  a  valve  having  no  lap, 
as  in  PL  XXIX.,  Fig.  1,  since,  as  is  evident  by  inspection,  a  full 
opening  of  j/,  for  instance,  for  exhaust  involves  a  simultaneous 
full  opening  of  p  for  admission.  But,  see  PL  XXIX.,  Fig.  4, 
when  the  valve  has  moved  to  the  left  till  p',  for  instance,  is 
fully  open  for  exhaust,  the  opening  at  p  will  be  less  than  the 
width  of  the  port  by  the  lap,  I.  If  this  opening  be  too  little, 
move  the  valve  still  further  to  the  left  by  a  greater  throw  of  the 


MACHINE   CONSTRUCTION   AND    DRAWING.  277 

eccentric,  till  the  required  opening  at  p  is  obtained,  and  con- 
trariwise, for  due  steam  opening  at  p' . 

Fourth.  Having  thus  the  proper  travel,  see  Theor.  XXYIIL, 
the  eccentric  can  be  set,  with  a  throw  just  equal  to  this  travel. 
The  action  of  the  valve,  by  which  the  port  p'  is  more  than 
opened,  for  exhaust,  in  order  to  secure  due  steam  opening,  as  at 
p,  is  advantageous,  since  it  keeps  p'  wide  open  for  exhaust  for 
more  than  a  bare  instant. 

Fifth.  While  a  port,  which  is  large  enough  to  afford  a  free 
exhaust,  need  not  be  fully  opened  for  the  admission  of  steam, 
still  it  will  do  no  harm  to  have  it  so  opened,  and  may  yield 
some  advantages,  especially  if  the  port  be  very  long  and 
narrow. 

When  the  travel  of  the  valve  is  quite  short,  the  valve  will 
move  more  slowly,  and  the  ports  will  be  opened  somewhat 
slowly,  and  the  steam  will  enter  with  some  difficulty  through 
the  very  narrow  opening  which  it  first  meets.  This  obstruction 
is  called  wire-drawing  the  steam.  It  may  be  avoided  by  in- 
creasing the  travel  and  hence  the  speed  of  the  valve,  so  that 
the  ports  will  be  rapidly  opened.  Also  by  making  the  outer 
edges  of  the  valve  quarter  round  instead  of  square,  as  at  k, 
Fig.  4. 

Increase  of  valve  travel,  so  as  to  give  a  port  opening  greater 
than  the  width  of  the  steam  port,  gives  the  further  advantage 
of  quicldy  bringing  the  ports  wide  open,  and  of  keeping  them 
so  during  that  part  of  the  travel  by  which  the  port  opening 
exceeds  the  width  of  the  steam  port.  This  excess  may  seem  a 
contradiction  in  terms,  but  the  port  opening  simply  means  the 
distance  which  the  outer  edge  of  the  valve,  as  f,  PL  XXIX., 
Fig.  5,  moves  from  the  outer  edge,  as  It! ,  of  the  port  to  its  ex- 
treme position,  which  may  be  to  some  point  as  f  beyond  the 
inner  edge  o,  of  the  port.  Thus  Jc'o  being  the  port,  kf  would 
be  the  port  opening. 

Sixth.  Exhaust  port  opening.  Whenever  an  inner  edge,  as 
?^,  Fig.  5,  of  the  valve,  being  at  mid-stroke  at  o,  moves  inwards 
towards  the  centre  line  BO,  a  greater  distance  than  the  width  of 
the  bridge  r,  it  partly  closes  the  exhaust  port  E.  Now,  to  secure 
a  proper  exhaust,  the  remaining  unclosed  portion  of  the  port,  E, 
must  be  at  least  equal  to  the  steam  port.  But  the  total  move- 
ment of  m,  from  o  to  the  left,  is  the  semi-travel,  and  thus  would 
bring  m  to  m'}  when  f  travels  to  f ,  m'f  being  simply  the  ex- 


273 


ELEMENTS    OF 


treme  left  position  of  mf.     We  thus  have  the  expression  for 
the  width  of  the  exhaust  port, 

E  =  om'  +m'n— r. 
=  om'  +  ok' — T. 

that  is,  E  =  the  semi-travel  +  the  steam  port  — 
the  bridge. 


Exhaust  Closure. 


e-  lap 


F.    I 


\ 


Summary  of  Elements. 

219.  The  main  particulars  hitherto  presented  can  be  conveni- 
ently impressed  upon  the  memory  by  a  diagram,  the  construc- 
tion of  which  is  sufficiently  illustrated  by  Fig.  106,  where  OB 
represents  the  crank  position,  and  AC  =  OB,  the  semi  valve- 
travel.  OA  represents  the  corresponding  position  of  the  eccen- 
tric arm  of  a  valve  without  lap  or  angular  advance.  It  is  there- 
fore the  line  from  which  (see  kn,  PI.  XXIX.,  Fig.  6)  the  lap 
angle  is  to  be  estimated. 

NoW,J?rs£,  suppose  an  angular  advance  of  20°  and  a  lap-angle 
also  of  20°  from  OA  (Prob.  XXY.)  giving  ae  for  the  lap  and 
ed  for  the  port  opening  (Th.  XXVIIL),  and  cut-off  at  50°,  and 
exhaust  closure  at  70°. 


MACHINE   CONSTRUCTION   AND   DRAWING.  279 

Then,  second,  let  the  angular  advance  be  increased  to  22£°, 
and  the  lap  angle  reduced  to  17£°  (Prob.  XXVIIL),  and  we 
shall  have —  ab  =  lap. 

be  =  lead. 
bd  =  port  opening. 
ad  —  semi-travel, 
exhaust  closure  at  67-|°,  and 
cut-off  at  50°. 

Or,  if  the  port  opening  =  ed,  as  before,  the  total  travel  will 
be  reduced  by  twice  the  reduction  of  the  lap.  Notice  that  be  is 
not  reckoned  for  the  5°  from  OA,  since,  in  fact,  the  angular  ad- 
vance is  made  first  from  h  to  &,  PI.  XXIX.,  Figs.  5,  6,  to  leave  the 
primitive  lap  angle  &B'n,  and  then  increased  to  give  the  semi- 
lead  angle,  between  the  full  and  dotted  lines  £B',  and  to  reduce 
the  lap  (Prob.  XXVIII.).  By  inside  clearance  =  be  (Th. 
XXIX.)  the  point  of  exhaust  closure  may  be  restored  to  70°. 

Upon  this  diagram,  it  is  only  necessary  to  remark : 

ls£.-Similar  illustrations  may  be  made,  beginning  with  any 
other  angular  advance  and  lap  angles,  taken  at  first  equal  to 
each  other. 

2e?.-IIaving  found  the  lap,  port  opening,  and  lead,  for  any 
travel,  the  same  can  be  found  for  any  other  travel,  by  the  sim- 
ple principle  that  they  are  all  proportional  to  the  travel.  For 
if  Fig.  106  were  reduced,  till  AC  were  any  given  part  of  what 
it  now  is,  all  parts  of  the  figure  would  be  reduced  in  the  same 
proportion. 

220.  The  matter  already  presented  enables  us  to  determine 
various  interesting  particulars.  The  piston  position  for  any 
given  crank  pin  position  can  easily  be  found,  as  already 
shown.  The  angular  advance  and  lap  angles  for  given  lead 
and  cut-off  being  given ;  the  travel,  and  the  eccentric  position 
for  any  crank-pin  position  can  readily  be  found,  and  the  valve 
position  for  any  given  eccentric  position  can  then  be  deter- 
mined, so  that  finally  the  valve  position  due  to  any  piston  posi- 
tion can  easily  be  constructed. 

Indeed,  the  student  cannot  now  better  exercise  himself  on 
this  subject,  than  by  constructing,  very  accurately,  and  on  a 
large  scale,  from  given  data,  taken  from  actual  practice,  a  fig- 
ure similar  to  PI.  XXIX.,  Fig.  5,  but  with  the  piston  positions 
for  all  the  crank  positions,  10°  apart,  and  for  those  at  5°  apart, 
near  the  dead  points ;  with  the  corresponding  valve  positions 


280  ELEMENTS   OF 

ranged  in  a  vertical  column,  and  all  referred  to  the  same  verti- 
cal centre  line,  or  plane,  BO. 

Another  most  useful  way  of  becoming  familiar  with  the 
relations  of  the  valve  edges  and  ports  in  all  positions,  is  to 
make  a  large  section,  like  any  of  the  sections  of  the  valve  and 
its  seat  on  PI.  XXIX.,  to  scale  from  measurements  (see  Fig. 
ri).  Then  cut  the  figure  apart  on  the  line  as  fg,  Fig.  1,  of  the 
valve  face,  and  move  the  valve  back  and  forth,  through  equal 
small  intervals,  which  will  clearly  show  its  relations  to  its 
ports. 

PROBLEM  XXX. 

To  Reverse  the  Motion  of  an  Engine. 
The  Drop  Hook  Motion. 

Referring  once  more  to  PI.  XXIX.,  Fig.  5,  with  crank-pin 
at  d.  moving  as  at  arrow  (1),  and  the  eccentric  centre  at  &, 
moving  the  valve  (rapidly)  to  the  left ;  let  a  second  eccentric 
be  placed  at  &",  where  k"t  =  Jet.  Let  the  rod  of  eccentric  It 
be  disconnected  from  the  rocker  H'J",  and  let  the  equal  rod 
from  k"  be  put  into  connection  with  H'5".  To.  do  so,  Ii'  will 
be  moved  to  s,  where  B"s  =  b"k",  and  the  rocker  will  appear 
at  ss'.  Then  lay  off  from  s'  the  distance  h"i,  and  it  will  give 
i',  the  new  position  of  the  valve  centre  (shown  on  S'F  carried 
vertically  upward  to  Fig.  n  to  avoid  further  confusion  of  the 
lower  figure).  All  the  edges  V I,  F,  etc.,  of  the  valve,  i'KIl(H) 
F,  and  its  ports,  are  projected  on  J'F,  Fig.  (ri). 

Then,  finally,  lay  off  on  each  side  of  i',  half  of  the  exterior 
length  J'F,  and  interior  length,  H,  of  the  valve,  and  we  shall 
have  its  position,  5"H'F',  when  in  connection  with  the  eccen- 
tric at  k". 

Before,  d  was  moving  as  at  arrow  (1),  the  piston  G  was 
moving  to  the  right,  by  the  expansion  of  the  steam  behind  (to 
the  left  of)  it,  the  exhaust  was  open  by  the  amount  ov,  and  the 
engine  was  going  forward. 

JVbw,  the  port  p  is  open  by  the  space  F'&',  the  port  p'  is 
wide  open  for  exhaust,  G  is  therefore  moving  to  the  left,  the 
crank-pin  d  is  moving  as  at  (2),  and  the  engine  is  going  hick- 
ward. 


MACHINE    CONSTRUCTION   AND   DRAWING. 


281 


Whence  we  conclude  that,  to  reverse  an  engine,  the  eccentric 
must  be  adjustable  upon  the  shaft,  as  from  k  to  ~k!' ;  or  there 
must  be  two  eccentrics,  as  at  k  and  k",  each  of  which,  sepa- 
rately, may  be  put  into  communication  with  the  rocker. 


The  latter  method  is  now  in  general  use. 

Formerly  the  eccentrics  were  separately  put  in  gear  with  the 
rocker  by  the  old  drop-hook  motion  still  seen  only  on  a  few  old 
engines,  though  generally  used  in  this  country  before  1850,  and 
often  previous  to  1860.  Space  forbids  more  than  the  mde 
illustration  of  it  in  Fig.  107,  the  study  of  which  will  greatly  add 
to  the  student's  appreciation  of  the  "  handiness "  of  the  link 
motion,  to  be  afterwards  briefly  explained. 


282  ELEMENTS    OF 

The  right-hand  view  is  as  it  would  appear  in  an  end  view  of 
the  engine,  and  the  other  is  as  appears  on  a  front  elevation  of 
the  engine. 

a — a' a"  is  the  rocker  shaft  in  two  parts,  one  on  each  side  of 
the  engine.  R,R'  — Rx//  the  lower,  and  Q,Q'  the  upper  rocker 
arm.  FH  is  the  forward  eccentric  rod,  or  rod  for  forward 
motion,  proceeding  from  an  eccentric  on  the  driving  shaft,  and 
now  behind  the  vertical  diameter  of  the  shaft,  as  R  is  drawn 
well  back.  BH  is  the  back  eccentric  hook,  out  of  gear.  Its 
eccentric,  now,  is  in  front  of  the  vertical  diameter  of  the  driv- 
ing shaft.  The  crank  pin  is  above  the  driving  shaft ;  the  valve, 
see  R  and  Q,  is  well  forward ;  steam  is  entering  the  rear  steam 
port,  that  is  the  one  nearest  the  shaft,  and  the  piston  and  the 
engine  are  moving  forward. 

To  reverse  the  engine,  draw  back  the  arm,  FG,  by  a  lever  in 
the  cab.  This  will  revolve  the  sector,  E,E',  and  thence  give 
the  small  gear,  DD',  half  a  revolution  on  its  shaft,  Dd,  also  the 
same  to  the  semi-circular  cams,  C— C',  and  c—c'.  This  opera- 
tion allows  BH,  which  rests,  by  its  stirrup  s,  on  the  cam,  cc',  to 
fall  by  its  own  weight;  and  raises  FH  off  the  rocker  pin,p,p'. 
Then,  by  drawing  back  the  arm,  /•/•',  by  a  lever  in  the  cab,  and 
through  the  rod  Mw,  the  rockers  are  revolved  to  the  position  K7<, 
where  the  hook,  A,  settles  on  to  the  pin,  pp",  revolved  to  the 
position  qp1' ' . 

The  valve,  being  then  in  a  position  to  admit  steam  to  the 
right-hand  end  of  the  cylinder,  while  the  crank  is  still  above  the 
shaft  as  before,  the  engine  will  go  backward  from  a  state  of 
rest,  when  before  it  would  have  gone  forward. 

The  eccentric  rods  being  side  by  side,  the  lower  rocker,  R,  is 
double,  as  shown  on  the  end  view ;  where,  to  avoid  confusion, 
the  end  view  of  the  eccentric  rods  is  omitted. 

This  was  not  a  very  rude  contrivance,  and  was  used  on  new 
first-class  express  passenger  engines  built  as  late  as  1857.  Still 
it  had  many  inconveniences.  The  hooks  (A)  might  bound  off 
their  pins,  or,  when  raised,  they  might  get  jambed  between  the 
rockers,  as  R'  and  R"  and  fail  to  fall  into  place  promptly  when 
the  cam  shaft  was  tumbled  over.  But  worst  of  all  was  the 
delay  when  instant  reversal  was  required.  For,  to  prevent  the 
rapid  oscillation  of  the  levers  in  the  cab,  for  swinging  over  the 
rock-shafts  in  reversing,  the  rod,  Mw.,  was  lifted  off  the  pin,  n,  by 
an  arm,  L,  drawn  to  an  upright  position  by  a  lever  acting 


MACHINE   CONSTRUCTION   AND   DRAWING.  283 

through  L£,  unless  the  latter  presented  a  ring  to  hand,  at  the 
cab.  Then  \st,  l&n,  must  be  settled  on  to  its  pin  on  the  arm,  r. 
2d.  The  cam  shaft  must  be  tumbled.  3d.  The  rockers,  K, 
must,  by  their  motion,  catch  the  hook  intended  for  them.  And, 
after  all,  from  a  scientific  point  of  view  again,  there  was 
no  cut-off,  at  least  no  variable  one.  Engines  iu  those  days  gen- 
erally had  little  or  no  lap  to  their  valves,  so  that  the  eccentrics 
were  essentially  at  right  angles  to  the  crank,  and  so  that  there 
was  no  cut-off,  or  but  very  little. 

Cut-offs,  then,  were  separate  valves,  in  separate  two-ported 
steam  (valve)  chests,  directly  over  the  main  valve  chest,  and 
were  generally  invariable  cut-offs  at  that.  This  required  one  or 
two  more  levers,  while  the  link  motion,  with  but  one  lever,  is  a 
variable  cut-off. 


EXAMPLE  LlX. 
A   Stephenson  Link,  Motion. 

Description. — This  motion  is  so  called  from  the  engineer 
who  first  brought  it  into  use.  It  was  invented  by  a  Mr.  Howe, 
an  Englishman. 

There  are  various  other  English  and  continental  link-motions. 
The  Gooch,  or  stationary  link,  except  as  to  its  oscillation  by  the 
eccentrics,  and  in  which  the  link  block  rises  and  falls  to  reverse 
an  engine.  The  Allan,  or  straight  link,  and  others. 

PI.  IX.,  Fig.  3,  is  merely  a  sketch  and  measurements  from 
a  link-motion  model,  not  showing  the  valve,  rocker,  and  eccen- 
trics in  their  true  relative  position,  but  which  may  quite  as 
well,  for  that,  illustrate  the  operations  of  drawing  such  a  model 
and  adjusting  it.  L  is  the  link,  and  to  catch  the  main  idea  of 
its  operation  it  is  only  necessary  to  conceive  the  forward  and 
back  eccentric  rods  in  the  last  example  to  be  attached  to  it 
as  at  f  and  5.  The  link  block  pin,  I,  is  held  by  the  lower 
end  of  the  rocker  arm,  R.  Then,  by  letting  down  the  link,  by 
the  hand-lever,  C,  working  on  the  arch,  A,  till  the  mean  posi- 
tions of  f  and  I  are  about  on  Qd,  the  forward  eccentric,  alone, 
will  actuate  the  valve.  But  if  the  link  be  raised,  till  5  and  I 
are  in  like  manner  together,  the  back  eccentric,  only,  operates  the 
valve,  essentially  as  in  the  drop-hook  motion,  only  that  but  one 
motion  of  one  lever  is  required  to  raise  or  lower  the  links  on 


284  ELEMENTS   OF 

both  sides  of  the  engine.  When  it  is  set  so  that  I  is  at  various 
points  between  b  and/,  I  will  have  the  resultant  motion  due  to 
the  joint  action  of  both  eccentrics.  The  effect  will  be  to  reduce 
the  travel,  and  hence,  obviously,  to  vary  the  cut-off,  by  the 
quicker  shutting  again  of  a  steam  port  after  it  begins  to  open. 

Thus  the  link  motion  is  a  variable  cut-off. 

Construction. — There  are  so  many  parts  and  points  to  a  link- 
motion,  that,  in  practice,  it  is  usual  to  fix  some  of  the  latter, 
with  reference  to  convenience  or  practicability,  as  governed  by 
surrounding  parts  of  the  engine. 

Thus,  taking  O,  the  centre  of  the  crank  shaft,  as  an  origin, 
or  fixed  point  of  reference,  and  Od  as  the  horizontal  centre  line, 
containing  the  axis  of  the  cylinder,  fix  T,  the  centre  of  the 
"tumbling  shaft"  by  the  co-ordinates  25f"  and  6^-ths,  in 
this  example.  Also,  S,  the  centre  of  the  rocker  shaft,  by  the 
co-ordinates  34"  and  4". 

The  fixed  dimensions  of  the  link  in  this  case,  are  the  radius 
of  its  central  arc,  the  "link- arc,"  34",  the  distance  between  the 
eccentric  rod  pins  5f ",  their  distance  back  of  the  link-arc  1£," 
and  the  length  of  the  saddle  4r|".  The  radius  of  the  link  arc 
must  =  the  eccentric  rod,  F/j  +  the  !•£"  just  mentioned,  to  avoid 
shifting  the  centre  of  the  travel,  in  different  "  gears." 

Let  the  travel  of  the  valve  be  2J".  For  this  purpose,  if  the 
rocker  arms  are  equal,  as  in  the  figures,  each  =  4^-",  the  half 
throw  of  the  eccentric,  or  radius  of  the  eccentric  centre,  will  be 
sensibly  1^",  or  half  the  travel. 

When  the  forward  gear  eccentric  rod,  F/,  is  in  action,  it  will 
be  nearly,  or  exactly,  on  the  centre  motion  line  Od,  and  when 
the  valve  V  is  at  its  extreme  left.  .  The  point  I,  the  link-ljloclt, 
pin,  which  is  held  by  the  lower  end  of  the  rocking  arm  R, 
must  then  be  at  its  extreme  right  or  34"  4-l$"=35$"  from  O. 
Hence  the  length  of  the  eccentric  rod,  as  I/,  from  the  eccentric 
centre  to/  must  be  35|—  (1$"  +  1$")  =  32$". 

The  distance  from  the  eccentric  centre  F,  to  the  outer  face  of 
the  collar  k,  Fig.  m,  of  the  eccentric  strap  being  4f  ",  the  length 
£/  of  the  eccentric  rod  proper  will  be  28$",  or  F  to  I  =  34". 

These  descriptions  show  the  relation  between  the  eccentric 
rods,  and  the  rocker  shaft  S.  That  is,  when  the  valve  is  at  mid- 
stroke,  the  rocker  arm  is  vertical,  usually,  and  the  link  block 
pin,  I,  must  then  be  at  the  same  horizontal  distance  from  O,  that 
the  point  S  is.  The  circle  O— FB  is  that  described  by  the  centres 


MACHINE   CONSTRUCTION   AND   DRAWING.  285 

of  the  eccentrics,  sensibly  of  !•§•"  radius,  for  a  travel  of  2^". 
The  position  of  I  can  be  found  for  any  assumed  valve  position. 

Let  us,  then,  consider  the  seven  leading  positions  of  Y  and  I. 

First.  When  the  valve  is  at  mid-stroke,  the  rocker  arms  will 
be  vertical,  and  any  motion,  either  way,  of  the  valve,  will  open 
an  exhaust  passage,  or  give  release  to  the  steam. 

Second.  If  V  be  drawn  each  way  from  mid-stroke  by  the 
amount  of  the  lap,  the  valve  will  be  at  the  points  where  cut  off 
takes  place,  and  I  will  be  at  positions,  which  we  will  call  l'l'lt 
Fig.  (y),  at  the  same  distance  on  the  opposite  sides  of  its  mid- 
position,  when  the  rocker  is  vertical. 

Third.  If  Y  loe  further  drawn  each  way  from  its  mid-position, 
by  the  amount  of  lead  proposed,  I  will  have  a  pair  of  positions 
I", I",,  at  the  same  additional  distance  each  way  from  its  mid- 
position.  That  is  the  horizontal  distance  from  I  to  l"=lap  + 


Now  the  last  pair  of  positions  of  the  valve  are,  of  course, 
those  which  occur  wnen  the  crank-pin  is  at  the  centre  or  dead 
points.  The  lead  must  then  be  the  same  at  one  port,  or  the 
other,  according  as  the  crank  pin  is  to  go  one  way  or  the  other. 
Hence  the  eccentric  centre  positions,  corresponding  to  I",  and 
l'\,  will  be  as  at  B'  and  F',  equidistant  from  D',  the  forward 
dead  point  of  the  crank  pin.  And  90°— F'OD'=90°— B'OD' 
will  be  the  angular  advance  of  the  eccentrics. 

This  gives  both  eccentrics,  crank,  and  valve  in  one  set  of 
simultaneous  positions.  If  the  link  be  dropped  into  place  for 
"full  gear  forward"  that  is,  for  forward  motion  of  the  engine, 
with  the  valve  moving  with  fall  stroke,  I  will  be  at  its  position 
I" „  Fig.  (?/),  and  the  required  lead  will  be  seen  in  the  amount 
of  opening  of  the  port^. 

Fourth.  Let  the  valve  finally  be  drawn  to  each  of  its  extreme 
positions,  and  we  shall  then  have  the  corresponding  extreme 
positions  I'"  and  l"\  of  the  link  block  pin  I. 

To  find  one  position  of  the  link. 

221.  By  (Theor.  XXX.)  knowing  the  travel,  or  diameter  of  O— 
FB,  the  lap,  and  the  lead,  F'  and  Br,  the  positions  of  the  eccen- 
tric centres,  when  the  crank  pin  is  at  D',  can  be  found  by  making 
their  perpendicular  distance  from  DO  =  the  lap  +  the  lead,  as 
just  now  indicated. 


2S6  ELEMENTS   OF 

Then,  from  F'  and  B'  as  centres,  with  radius  equal  to  the 
length  to  f  and  5,  32£",  in  this  case,  describe  arcs,  which  will 
contain  the  points  f  and  b,  as  the  link  rises  and  falls. 

When  F'  and  B'  are  the  eccentric  centres,  the  points  f  and  b 
will  have  one  pair  of  positions  at  a  perpendicular  distance  from 
Od,  on  each  side  of  it,  equal  to  half  fb  or  2-^£".  Then  draw  lines 
.parallel  to  Od,  at  this  distance  from  it,  and  note  where  they 
intersect  the  arcs  before  drawn  from  F'  and  B'  as  centres.  An 
arc,  through  the  positions  of  f  and  5,  thus  found,  with  32^" 
radius,  will  have  its  centre,  Q,  (not  shown)  on  Od,  and  an  arc  of 
34:"  radius,  and  Q  as  a  centre,  will  be  one  position  of  the  link 
arc. 

Data  for  finding  any  position  of  the  link. 

222.  1st.  F  and  B  are  always  on  the  circle  FBF',  and  at  a 
chord  distance  apart  =  F'B',  as  previously  found. 

2d.  f  and  b  are  at  a  constant  distance  apart. 

3d.  Ff  and  BJ  are  of  constant  length,  for  any  one  arrange- 
ment of  the  model. 

4th.  s,  the  saddle-pin,  forms  with  f  and  b  a  known  triangle, 
fsb,  where  fs  may  be  less  than  bs,  to  reduce  the  slip  of  the  block 
in  the  link,  the  path  of  b  being  more  nearly  parallel  to  that  of  I. 

5th.  T  being  a  rigid  joint,  and  t  a  flexible  one,  the  different 
positions  of  6-  will  all  be  on  an  arc  with  t  as  a  centre,  and 
radius  ts,  in  this  case  of  T'. 

6th.  The  centre  from  which  the  link  arc  is  described  is 
always  on  a  perpendicular  tofb,  at  its  middle  point. 

With  these  data,  the  student  is  left  to  construct  various  posi- 
tions of  the  link,  either  by  intersections  of  lines,  or  by  a  slip  of 
stiff  paper  or  thin  wood,  cut  to  fit  the  curve  of  the  link  arc,  and 
on  which  the  points/",  b  and  s  are  fixed. 

For  any  position  of  the  link,  I  is  always  the  intersection  of  the 
link  arc,  with  the  arc  described  by  I  from  S  as  a  centre,  with 
the  rocker  arm,  R,  as  a  radius,  4^-",  in  this  example. 

When  the  valve  rod  is  attached  directly  to  I,  slip  is  avoided, 
as  Zeuner  shows,  by  making  ts  and  tT,  each,  half  of  a  parallelo- 
gram, turning  on  two  opposite  centres  of  which  T  is  one,  while 
the  side  ts  carries  a  slotted  guide  in  which  *  moves  horizontally 
in  all  gears,  and  thus  without  vertical  motion  of  the  link. 


MACHINE   CONSTRUCTION  AND  DRAWING.  287 

To  adjust  the  Model. 

223.  The  several  adjustable  arms  and  rods  are  telescopic,  and 
fitted  with  clamps  to  adjust  their  length. 

First.  To  adjust  the  Travel.  Set  the  fixed  measurements  as 
given,  to  locate  T  and  S,  and  fix  the  lengths,  F/,  and  BJ,  and 
make  si  =  %'.  Drop  the  link  into  the  full-gear-forward  position, 
and  make  the  half -throw  of  each  eccentric  =  half  the  proposed 
travel,  and  set  both  eccentrics  as  nearly  as  possible  to  their  in- 
tended positions,  as  F'  and  B'  for  the  crank  at  D',  according  to 
the  lap  and  lead  required.  Turn  the  crank  till  the  vertical 
centre  line  of  the  valve  coincides  with  VII,  that  of  the 
cylinder.  Then  turn  the  crank  carefully  and  measure  the  dis- 
tances of  the  extreme  positions  of  the  valve  centre  from  Vtl. 
If  their  sum  varies  from  the  travel  (2J")  alter  the  half -throw  of 
the  eccentric  by  half  the  error  till  the  required  amount  of  travel 
is  secured.  Then  if  these  distances  are  unequal,  alter  the  length 
of  the  valve  stem,  ab,  till  they  become  equal.  Thus,  if  the 
valve  move  further  to  the  right  of  VH  than  to  the  left,  we 
should  lengthen  the  valve  stem  by  half  the  difference. 

The  amount  and  equalization  of  the  travel  for  one  eccentric 
are  now  accomplished,  but  without  regard  to  the  relative  posi- 
tion of  the  valve  and  piston.  That  will  next  be  attended  to. 

Second.  To  give  a  certain  lead  to  the  valve.  This  is  accom- 
plished by  the  angular  movement,  only,  of  the  eccentric.  Then 
clamp  the  crank  at  CD',  unclamp  the  eccentric,  F,  and  rotate  it 
on  its  shaft  till  the  port  p  is  open  the  desired  amount,  -£$". 
Then  clamp  it.  Then,  if  the  crank  be  clamped  at  OD",  the  lead 
at p'  will  be  the  same,  and  for  a  single  eccentric  the  adjust- 
ment will  be  complete. 

Third.  To  adjust  the  backward  gear,  B5,  etc. 

1st.  Test  the  amount  of  travel,  and  perfect  the  throw  of  the 
eccentric,  B. 

2d.  Test  the  equality  of  travel  each  way  from  VH,  and  if 
unequal,  equalize  it  by  a  slight  adjustment  of  the  length  of  B&, 
since  to  alter  the  valve  stem  would  disturb  the  equalized  travel 
of  the  forward  gear. 

3d.  Clamp  the  crank  at  OD',  and  rotate  the  back  eccentric 
till  a  lead  of  -fa"  appears  at  p,  and  clamp  it,  when,  if  the  crank 
be  revolved  to  OD",  the  same  lead  should  appear  at^>'. 

Fourth.  To  readjust  the  full  gear  forward.  The  adjustment  of 


288  ELEMENTS   OF 

the  gear  backward  will  sometimes  a  little  disturb  that  of  the  for- 
ward gear.  If  so,  re-equalize  the  travel  by  a  slight  adjustment 
of  the  length  of  Ff.  Then  reset  the  lead  by  a  small  angular 
movement  of  the  eccentric,  the  crank  being  at  OD'  or  OD". 

Remarks. — The  foregoing  operations  are  easy,  yet  may  be- 
come tiresome  by  overlooking  some  little  practical  points.  Clamp 
each  fixed  part  tightly.  The  rocker  arms  should  be  vertical  at 
mid-stroke  of  the  valve.  See  that  the  eccentric  rods  are  of  the 
proper  length  and  do  not  slip.  Let  the  points  /"and  I  be  about 
in  a  horizontal  line  in  the  extreme  forward  position  of  the  eccen- 
tric. If  the  crank  overpasses  a  dead  point  where  it  should  stop, 
'do  not  lack  it  up  to  the  point,  but  go  back  some  distance  and 
then  come  forward  to  the  point.  This  is  to  "  take  up  the  lost 
motion,"  or  play  between  parts  at  all  the  joints. 

224.  When  the  model  is  finally  adjusted,  the  valve  can  be  set 
by  turning  the  crank  at  the  points — of  beginning  to  open  a  steam 
port  ;  cutting  off ;  exhaust  closure,  or  beginning  of  compression  ; 
and  of  release,  or  end  of  expansion,  and  the  corresponding  piston 
positions  can  be  noted  on  the  scale  II  for — Full  gear  forward ; 
full  gear  backward,  and  any  intermediate  gear. 

The  model  being  adjustable  in  all  parts,  other  travels  may  be 
taken.  The  following  are  specimen  results  :  Lap  —  £". 

1°— Full  Gear  Forward.     Travel  =  1£". 

Lead =  TV'  at  each  end. 

Front  port  opening,^  =  fg".     Back  port  opening,^'  — -jV 

Cut  off  at =  17,4"  (half  inches)  forward  stroke. 

"     "     " =  16.7        "         "        backward     " 

2°— Partial  Gear  Forward.     Travel,  1J". 

Front.  Back, 

Lead A"  A" 

Cut  off 6.1  (half  ins.)      6.4  (half  ins.) 

Opening ft  & 

3°— Full  Gear  Forward.     Travel,  2J". 

Front.  Back. 

Lead ^  iV 

Cut  off  at 19  (half  ins.)      18.75  (half  ins.) 

Opening full.  full. 


MACHINE   CONSTRUCTION   AND   DRAWING. 


—  Full  Gear  Backward. 

Front.  Back. 


Lead 


Cut  off  ..............   19f  (half  ins.)     19  (half  ins.) 

Opening  ............   full.  full. 

Again,  in  a  little  different  form,  and  more  fully. 

5°—  Travel  1£",  Stroke  12"  =  24  half  ins. 


Full  Gear  Forward. 


Front  End. 

Back  End. 

Front  End. 

Back  End. 

Lead 

V" 

-V' 

J* 

t 

Opening  

4#" 

H 

X" 

If" 

Cut-off  in  |  ins  .  .  . 

18.2 

17.6 

IS.9 

ie.7 

Full  Gear  Backward. 


6°— Travel  2^",  Stroke  12"=24  half  ins. 


FuU  Gear  Forward. 

FuU  Gear  Backward. 

Forward 

Stroke. 

Backward 
Stroke. 

Forward 
Stroke. 

Backward 
Stroke. 

Lead 

-rV 

iV 

ft 

19.2 

22.5 

iV- 

ilss 

22.6 

r 

19.45 
22.6 

Openincr 

T^T 

Cut-off  r  

Compression 

t  i  j  id- 

j  ins.  \  22.4 

7° — Partial  or  Mixed  Gear.     Travel  reduced  to  1-jV'. 


Forward  Motion  or  Gear. 

Backward  Motion  or  Gear. 

Forward  Stroke  or  End. 

Backward 
Stroke  or  End. 

Forward 
Stroke  or  End. 

Backward 
Stroke  or  End. 

Lead                   .        $" 

¥' 

ft" 

19.6 

»- 
ft" 

19.25 

A" 

12 
19.6 

Opening  TV  ' 
Cut-off  )    i    (  12." 
Compression  j  ins.  \  19.3 

19 


290  ELEMENTS    OF 

"Throw  "  is  differently  defined  as  the  radius,  or  the  diameter 
(208)  of  the  circle  made  by  the  eccentric  centre.  Either  way 
has  its  convenience.  The  question,  "  how  far  will  the  eccentric 
throw  anything,"  gives  the  answer  throw  —  the  diameter  named. 

With  this  summary  account,  the  reader  is  referred  to  the 
works  of  Auchincloss,  Zeuner,  Colburn,  and  others,  in  which  this 
and  other  link  motions  are  more  fully  treated  than  is  possible 
or  necessary  here. 

By  now  putting  together  the  eccentric,  with  its  straps  and 
rods,  Ex.  XXIX. ;  the  link,  Ex.  XXVIII. ;  the  cylinder,  Ex. 
X. ;  and .  valve,  Ex.  XLII. ;  with  the  valve  stem  and  rockers, 
the  student  can  draw  a  valve  motion,  from  which  he  can  learn 
much.  The  following  may  afford  further  data  for  practice  in 
drawing,  while  the  tables  annexed  are  interesting  as  experi- 
mental determinations  of  the  best  relative  positions  of,  points  of 
the  link  for  making  the  main  events  of  each  stroke  alike. 


EXAMPLE  LX. 
Data  of  Valve  Motions. 

I. —  Valve  Motion  of  a  15"  x  22"  Cylinder  Passenger  Engine  : 
Atlantic  and  Gt.  Western  E.  B. 

Length  of  connecting  rod =  6'-10y 

Centre  of  shaft  to  centre  of  rocker =  5'-  9f  " 

"  line  of  engine  to  centre  of  rocker,  vertically  =  5£" 
"  line  of  link  to  centre  of  eccentric  rod  pin. . . .  =  3g" 
"  of  tumbling  shaft,  from  centre  of  driving  axle, 

horizontally =  4'-  4$" 

"      of  tumbling  shaft,  above  centre  line  of  engine  =       lOf " 

Radius  of  link,  centre  arc =  5'-  81" 

Length  of  suspending  link —       13V 

Distance  between  centres  of  eccentric  rod  pins =       11£" 

Saddle  pin  back  of  link  arc =  L" 

Lower  rocker  arm  out  of  centre,  towards  axle 
Length  of  eccentric  rod 

Travel  of  valve ==  4"     Kocker  arms,  each.  =         9f " 

Outside  lap =          £ "     Bridges 1$"  x  15" 

Inside  lap =  0       Exhaust  port 2  "  x  15' 

Steam  ports 1  "  x  15"     Drivers,  diameter.  .  =    5'-  0" 


MACHINE    CONSTRUCTION   AND    DRAWING.  291 

11. —  Valve  Motion  of  a  16"  x  24"  Cylinder  Passenger  Engine  : 
New  York  G.  and  Hudson  River  12.  JR. 

Length  of  connecting  rod T—  5  J" 

Centre  of  shaft  to  centre  of  rocker,  horizontally. . . .  5'-     3" 

"       "  rock-shaft  above  centre  line  of  Cyl 6f " 

Eccentric  rod  pin  back  of  centre  arc  of  link 3£" 

Centre  of  tumbling  shaft,  from  centre  of  main  axle, 

horizontally 3'-  7$" 

Centre  of  tumbling  shaft,  below  centre  line  of  engine  V-  3£" 

Radius  of  link  arc 5'-     3" 

Length  of  supporting  link V-     2" 

Lower  rocker  pin  out  of  centre  towards  axle -jV' 

Saddle  pin  back  of  link  arc T\" 

Length  of  eccentric  rods,  centre  of  eccentric  to  centre 

of  eccentric  rod,  =  knuckle  joint,  pins 4'-ll£" 

Eccentric  rod  pins,  apart     13"     Rocker  arms,  each  .  9" 

Travel  of  valve....               5"     Bridges 1" 

Outside  lap $"     Exhaust  port 2f "  x  14J" 

Inside  lap •£$"     Four    coupled    dri- 

Steam  ports 1£"  x  14J"         vers,  Diana 5'-     2" 

III. —  Valve  Motion  of  an  18"  x  22"  Cylinder  Freight  Engine  : 
N.  T.  C.  and  Hudson  River  R.  R. 

Steam  ports If"  x  15"     Outside  lap f " 

Bridges 1J"     Inside  lap -fa" 

Exhaust  port 3"  x  15"     Eccentric,  diam. .  .  .  $£§>" 

Valve  travel 5"     Length  of  rockers.  .  9" 

Hor.  dist.,  centre  of  main  axle  to  centre  of  rock-shaft .  55" 

Centre  of  rock-shaft  above  centre  line  of  engine ....  8-|" 

Radius  of  link,  centre  arc 50" 

Saddle  pin  back  of  link  arc -J" 

Length  of  eccentric  rods,  as  above  (II.) 

Eccentric  rod  pins,  =  knuckle  joints,  apart 

«             "         back  of  link  arc 3£" 

Centre  of  eccentric  to  link  arc 55£" 

Hor.  Dist.  of  lifting  (tumbling)  shaft  from  centre  of 

driver 36f  " 

Centre  of  lifting  shaft  below  centre  line  of  engine .  .  14" 

Length  of  lifting  arm 18" 

Six  coupled  drivers,  Diam 4'-     9" 


ELEMENTS   OF 


Determination  of  weH  adjusted  [  Valve  Motion  for  a  15"  x  22" 


Forward  Motion. 

Back  Motion. 

Forward  Stroke. 

Backward  Stroke. 

Forward  Stroke. 

Backward  Stroke. 

1 

c 

t 

£ 

g 

1 

di 

r 

O 

Cut  off. 

! 

I 

Opening. 

1  Cutoff. 

! 

i 

I 

t 

1 

.i 

te 

| 

s 

ii 

J 

I 

Valve  Trn 

-! 

I 

J 

1 

"§ 
O 

CENTRE  OF  SADDLE  DIRECTLY  OVER  CENTRE  LINE  OF  LINK. 


[Cut 

full 

full 

<>if 

=1" 

18*" 

1" 

,V 

=1" 

18| 

1" 

4" 

4" 

< 

-T 

umb 

ling 

•b 

Btt 

ixm 

= 

o  • 

1 

164 
144 

2' 
3 

i 

A 

| 

24" 
34 

t 

III 

•fa 

4] 

ft 

ft 

4f 

14 

84 

A 

91 
71 

5 
0 

f 

ft 

?" 

n  i 

CENTRE  OF  SADDLE  -fa"  FROM  CENTRE  LINE  OF  LINK. 


I 


m 


154  11 
13424 
114  34 
9i 

7:1 


r 


A  ;• 

If 
®j 


184  1 

13*3* 
12434 
10*44 
8|5i 


1 4" 
0   3 

!   *2f* 
•*2ft 


H2v 


CENTRE  OF  SADDLE  *"  FROM  CENTRE  LINE  OF  LINK 


8* 


H 


tV 


10 


H 


2 


84 


ffilfull. 


19 
15111 


14 


1143* 


,>. 


5| 


18f  1 
J5t21 


11431  0 


±2* 
12ft 


CENTRE  OF  SADDLE  -,V  FROM  CENTRE  LINE  OF  LINK. 


full. 

1 
i 
ft 


8* 


2411 

2*11 


3* 

5 

ml 


74 


u 


131  2f 
114  3* 

9i  4^ 


5* 


r 

1841 
154  2* 
14   3 

11*34 
104  5 
8451 


I 

*|2* 
418ft 


MACHINE   CONSTRUCTION    AND    DRAWING. 


293 


Cylinder  Engine,]  by  successive  experimental  approximations. 


Forward  Motion. 

Back  Motion. 

Forward  Stroke. 

Backward  Stroke. 

Forward  Stroke. 

Backward  Stroke. 

| 

c 

1 

I 

§ 

i 
I 

Opening. 

Cut  off. 

a 

0 

I 

1 
I 
O 

Cutoff. 

! 

5 

VnlveTn 

1 

| 

1  Cutoff. 

I 

z" 

1  Cutoff. 

f 
O 

Differenc 

CENTRE  OP  SADDLE  *"  FROM  CENTRE  LINE  OF  LINK. 


fuU. 


64 


full 


18J 


74 


'% 

14*  24 
12  ,3* 
10  4± 
8  54 


ftM.  I8f  1 
*  I H  15*  2 
'  '  '  13*J3 

12  14 


ft    i    -  r 
ft1  ft  HO  44 
&!  I  I  8£54 


0 

0 

*2f 


6.  CENTRE  OF  SADDLE  -,V  FROM  CENTRE  LINE  OF  LINK.     TUMBLING  SHAFT-ARM  =  17' 


ft 

full. 

18" 

14 

full. 

ist 

1 

I 

34 

I 

II 

i 

tt 

16* 

2 

£ 

13. 

Hii 

14 

-f 

A 

ft 

13-J 

2| 

^L. 

ft 

14 

4 

2* 

A; 

81 

. 

4 

124 

34 

2A 

• 

7.    CENTRE  OF  SADDLE  -,V  FROM  CENTRE  LINE  OF  LINK.     TUMBLING  SHAFT-ABM,  17f ". 


full. 


A 


If 


"» 

« 


10 


full. 

* 


18* 


10  I  *  i* 


3ft 
*24 
24 

*8 


ft 


full.  19*  | 
H  F*  2 
-,a,r  13*!  24 
ft  H*J3* 
I  941 4* 
ft  7454 


Atlcentre  nlotchi,^   Mid 


18*1 

15|2| 


11*4 
945 
74(6 


i" 


4' 


T 


Inspection  of  this  table  shows  that,  as  the  link  approaches  its  mid- 
gear  position,  lead  increases ;  port-opening  and  travel  diminish,  and 
cut-off  and  compression  occur  sooner.  The  crank  being  at  CD',  or 
OD",  lead  occurs.  The  eccentrics  will  be  at  F'  and  B'  and  lead  is 
greatest  at  mid-gear,  because,  see  PI.  XXXIII.,  Fig.  4,  shifting  the 
link  to  mid-gear  advances  it  a  little,  but  withdraws  it  when  the  crank 
is  at  OD".  thus  opening  the  ports  more,  at p  and p',  respectively. 


294  ELEMENTS   OF 


"Setting"  the  Valve  Motion  of  a  Locomotive* 

225.  The  engineer  in  charge  first  locates  his  cylinders  and 
steam  chests,  places  the  valves  on  their  seats,  and  the  yokes 
(with  their  stems)  over  them.  The  drivers  and  axles  (eccentric 
pulleys  being  on)  are  fitted  to  their  boxes.  Guide  rods,  one 
cross  head,  and  connecting  rod,  tumbling  shafts  and  springs, 
rocker  boxes  and  rockers,  located  according  to  the  drawings. 
The  links,  with  their  saddles  attached,  are  swung  from  the 
tumbling  shaft  by  their  suspending  links.  The  link  blocks  are 
then  fastened  to  their  respective  rockers. 

The  Engineer,  having  attached  the  stub  ends  of  the  eccentric 
rods  to  the  straps  and  links,  prepares  a  trammel,  and  centre 
punch  points,  to  indicate  for  the  smith  the  proper  length  to 
which  the  rods  should  be  "  pieced  out."  They  are  subsequent- 
ly put  in  position.  The  reversing  lever  is  mounted,  as  well  as 
the  unslotted  arches ;  the  tumbling  shaft  is  ready  for  its  con- 
necting rod  to  form  its  attachment  with  the  reversing  lever. 
This  rod  is  "  pieced  out  "  to  the  length  indicated,  by  dropping 
the  link  into  extreme  gear,  and  observing  how  far  over  the  re- 
versing lever  is  capable  of  motion  without  interference  with  the 
cab. 

There  is  no  occasion  to  place  the  pistons  or  their  rods,  but 
simply  to  take  all  dimensions  which  have  reference  to  its  mo- 
tion, from  centre  punch  marks  on  the  cross  head. 

The  engine  is  then  "  jacked  up "  under  the  boxes  of  the 
drivers,  so  that  the  latter  clear  the  track.  The  first  step  in  the 
process  of  alignment  is  to  mark  the  quadrant  points  on  the 
drivers,  with  reference  to  an  arm  clamped  on  the  main  frame 
which  will  so  overlap  the  face  of  the  driver  that  the  passage  of 
the  point  during  the  revolution  of  the  wheel  will  be  noted  very 
distinctly. 

The  driver  is  now  connected  with  the  cross  head  ;  then  it  is 
revolved  until  the  latter  reaches  the  end  of  its  stroke,  and  this 
extreme  point  is  marked  on  the  guide  rods.  Distant  about  2" 
from  this  point  along  the  rod  another  centre  punch  mark  is 
made.  Then,  after  revolving  the  drivers,  their  motion  is  arrest- 
ed when  the  end  of  the  cross  head  arrives  at  this  second  point ; 
while  stationary,  the  "  scriber  "  is  drawn  along  the  overlapping 

*  By  W.  S.  Auchincloa,  0.  E. 


MACHINE    CONSTRUCTION   AND   DRAWING.  295 

arm,  and  a  line  marked  on  the  face  of  the  driver.  Upon  re- 
volving the  drivers,  their  motion  is  arrested  when  the  points  are 
a  second  time  in  alignment,  and  the  face  of  the  wheel  is  scribed 
as  before.  We  thus  have  2  points  on  the  face  of  the  wheel 
equally  distant  from  the  point  when  the  crank-pin  is  on  one  of 
the  "  centres  "  or  dead  points.  Therefore  the  bisection  of  this 
arc  gives  a  point,  which,  placed  immediately  under  the  scribing 
edge  of  the  arm,  will  place  the  crank  pin  on  the  "  centre." 

By  repeating  this  process  with  the  cross  head  when  at  the 
other  end  of  the  guides,  we  are  able  accurately  to  find  the  other 
"  centre."  Thus  obtaining  the  "  centres "  on  the  face  of  one 
d  liver,  we  can  readily  "train  "the  quadrants.  The  strap  of 
the  connecting  rod  is  next  removed,  and  the  rod  allowed  to  rest 
on  its  yoke. 

With  these  four  points  carefully  determined,  we  are  able  at 
any  moment  to  "  pinch  "  the  crank  pins  of  either  cylinder  over 
to  their  "  centres." 

The  eccentric  pulleys  are  then  placed  with  nearly  the  proper 
amount  of  lead  (as  nearly  as  the  eye  can  judge),  the  reversing 
lever  thrown  into  full  gear  forward,  and  the  drivers  "  pinched  " 
until  one  of  the  crank  pins  is  on  its  centre. 

It  should  here  be  observed,  that  instead  of  measuring  the 
lead  directly  from  the  valve  and  the  edge  of  its  port  with  steam- 
chest  bonnet  off,  it  is  customary  after  the  valve  is  scraped 
to  its  seat,  1st,  to  place  it  so  that  on  one  side  the  steam  port  is 
just  closed,  and  having  made  a  centre  punch  hole  on  the  face 
of  the  stuffing-box  flange,  place  the  small  leg  of  the  valve  gauge 
in  it ;  with  the  other  leg  scribe  a  line  on  the  valve-stem,  on 
which  line  make  another  centre  punch  hole.  2nd,  place  the 
valve  so  that  the  opposite  port  is  just  closed,  and  make  a  second 
centre  punch  hole  on  the  valve  stem,  as  will  be  indicated  by  the 
valve  gauge.  This  gauge  is  made  of  a 
small  piece  of  square  steel  bent  thus,  Fig.  (t  I  ) 

108,   and    sharply  pointed   on   the  legs.    |  [/ 

One  of  these  accompanies  each  engine. 
It  is  thus  apparent  that  the  engineer  can 
(in  the  case  of  the  eccentric  pulley  slip- 
ping)  readjust  his  valve  with  the  proper 
lead  without  removing  the  steam-chest  bonnet. 

The  lead  the  valve  now  has  is  noted  in  the  forward  and  back 
stroke ;  if  not  equal,  it  is  made  so  by  adjusting  the  length  of 


296  ELEMENTS    OF 

the  valve  stem,  by  turning  the  right  and  left  nut,  which  connects 
its  two  parts,  and  then  locking  the  check  nuts.  The  forward 
eccentric  pulley  is  then  altered  until  it  gives  the  required  lead. 
This  operation  is  performed  on  both  sides  of  the  engine  until  a 
perfectly  "  square  "  motion  is  obtained  in  forward  gear. 

After  this,  the  point  at  which  the  reversing  lever  lock  bolt 
strikes  the  arches  is  carefully  marked  with  a  scriber,  and  the 
lever  is  thrown  into  full  gear  back. 

If,  on  trial,  it  appears  that  the  motion  is  not  a  "  square"  one, 
it  will  be  necessary  to  introduce  a  slip  of  sheet  iron  between  the 
head  of  the  backing  eccentric  rod  and  the  eccentric  strap ;  then 
draw  the  bolts  tightly  together.  This  slip  should  just  equal  in 
thickness  half  the  difference  between  the  leads.  After  this 
adjustment  results  in  a  "square"  motion,  the  backing  eccentric 
should  be  altered,  until  the  same  lead  is  produced  in  full  gear 
back  as  was  given  in  full  gear  forward. 

Having  repeated  this  process  on  both  valves,  the  arches  should 
be  marked.  In  order  to  insure  perfect  accuracy,  the  lead  and 
"  squareness "  of  the  valve  in  forward  motion  should  be  re- 
examined,  in  order  to  guard  against  any  disarrangement  which 
may  have  occurred  while  adjusting  the  back  motion. 

It  now  remains  to  mark  the  other  "notches."  These  for  a 
24"  cylinder  are  usually  8",  10'',  12",  16",  20",  22",  and  indicate 
the  points  of  cut-off  when  the  reversing  lever  is  in  either  notch. 
They  may  be  accurately  described,  by  again  attaching  the  con- 
necting rod  to  the  driver  and  cross-head,  then  laying  off  the 
points  from  the  end  of  the  stroke  as  shown  on  the  guides ;  pinch- 
ing over  the  driver  until  the  cross-head  mark  corresponds  with 
either  of  these  and  drawing  back  the  reversing  lever  until  the 
valve  just  closes  the  port.  At  this  point,  mark  the  arches  and 
so  continue  to  obtain  the  other  points.  The  centre  notch  will  be 
found  at  the  point  of  bisection  of  the  arches  between  the  two 
points  of  shortest  cut-off.  Finally  slot  the  "  notches "  in  the 
arches. 

It  only  remains  to  rigidly  attach  the  eccentric  pulleys  to  the 
driving  axle.  This  is  done  by  scribing  the  position  of  the 
feather  on  the  pulley  ribs  and  the  axle ;  then  sinking  a  f"  square 
feather — J"  into  the  axle  f "  into  the  pulley,  driving  in  solid. 
Also  by  letting  the  points  of  the  two  steel  f- "  set  screws  into  the 
axle  through  each  pulley. 


MACHINE   CONSTRUCTION   AND   DRAWING.  297 

REGULATORS. 
'  Governors. 

Elementary  Principles . 

226.  A  comprehensive  idea  of  the  governors  used  in  equaliz- 
ing the  speed  of  steam  engines,  water  wheels,  etc.,  may  best  be 
had,  at  the  outset,  by  considering  the  different  principal  ways 
in  which  they  may  be  classified. 

In  respect  to  the  essential  governing  member  of  the  con- 
trivance there  are — 

1.  Ball  governors,  the  most  familiar  kind. 

2.  Fan  governors,  in  which  the  resistance  of  the  air 
to  an  increased  speed  of  revolving  vanes,  is  made  to  diminish 
the  steam  passages. 

3.  Oil  governors,  in  which  the  increased  velocity  of 
a  paddle  wheel  or  propeller,  working  in  oil  is  made  to  act  to 
produce  the  same  effect. 

In  respect  to  the  point  at  which  the  governor  takes  effect 
there  are — 

I.  Throttle  governors,  acting  to  close  a  valve  in  the  steam 

pipe. 
II.  Steam  valve  governors. 

227.  The  popular  idea  of  an  engine  governor  is  that  it  is  a 
contrivance  for  rendering  the  speed  of  the   engine   uniform 
under  a  variable  load. 

It  is  true,  that  it  will  maintain  an  unvarying  speed  under  a 
uniform  load,  and  with  a  uniform  steam  pressure  ;  and  further- 
more, that  it  will  maintain  a  uniform  average  speed  under,  a 
uniform  average  load.  But  it  will  not  maintain  an  unchanged 
speed,  if  the  load  be  permanently  increased  or  diminished, 
though  it  will,  by  virtue  of  the  consequent  diminution  or  in- 
crease, respectively,  of  the  speed,  so  increase  or  diminish  the 
steam  supply  delivered  to  the  piston,  as  to  make  the  alteration 
of  speed  by  the  alteration  of  load  less  than  would  naturally 
result  without  a  governor.  In  other  words,  it  holds  the  engine 
from  "  running  away,"  as  it  is  called,  if  the  load  be  greatly 
diminished;  prevents  it  from  stopping,  if  the  load  be  corre- 


298 


ELEMENTS    OF 


spondingly  increased,  and  makes  the  speed  more  nearly,  some- 
times much  more  nearly,  uniform,  under  a  variable  load,  than  it 
would  be  without  one. 

228.  Of  the  inherent  defects  in  the  simple  ball  governor,  and 
of  the  methods  of  overcoming  them. 

Fig.  109  represents  a  sleleton  ball  governor,  where  the  lowest 


and  highest  positions  are  on  the  lines  0  and  6.  B  and  C  are 
fixed  points,  so  that  as  the  balls  rise,  a  forked,  or  toothed 
top,  at  A,  depresses  the  valve  Y  and  closes  the  steam  pipe. 
Now  if  the  balls  rose  through  equal  heights  for  equal  incre- 
ments of  speed,  the  valve  would  be  proportionally  closed.  But 
they  do  not,  on  account  of  the  greater  lever  arm  with  which 
the  weight  of  the  ball  acts  to  depress  the  ball  from  its  higher 
positions. 

229.  One  method  of  neutralizing  this  defect  is,  to  give  the 
balls  a  short  range  of  action,  as  from  line  4  to  line  6,  only,  and 
a  high  velocity,  say  60  revolutions  to  30  of  the  engine,  so  as  to 
keep  them  in  a  high  position.  Then,  as  the  entire  arc,  through 
which  they  act,  approaches  to  a  vertical  direction,  equal  incre- 
ments of  velocity  will  elevate  the  balls  by  nearly  equal  amounts. 

A  second  method  of  compensation  is  to  balance  the  gover- 


MACHINE    CONSTRUCTION    AND    DRAWING.  299 

nor  balls  by  a  weighted  arm,  and  so  to  hang  the  governor 
by  jointed  arms,  that  they  remain  in  a  horizontal  plane,  and  all 
work  of  lifting  them  ceases,  and  only  the  resistance  of  their 
inertia  to  an  increased  velocity  in  their  plane  remains. 

An  example  of  this  construction  will  presently  be  given. 

Finally,  the  principle  of  graduation,  used  in  the  cele- 
brated Judson  governor's,  has  been  employed  in  connection 
with  the  first  method  of  compensation  just  described.  This 
principle  consists  in  shaping  the  steam  openings,  which  are 
regulated  by  the  governor  valve,  not  as  rectangles,  but  as  a 
tapered  opening,  so  adjusted  that  equal  increments  of  engine 
velocity  will  cause  the  governor  through  rising  by  decreasing 
increments  of  height,  to  shut  off  equal  successive  areas  of  steam 
port  in  the  governor  valve  seat. 

On  the  other  hand,  some  governors  abandon  the  ball  regulator ; 
examples  of  such  will  be  described  presently. 

230.  In  regard,  now,  to  the  second  classification  (226).   The  es- 
sential idea  of  the  class  of  throttle  governors  is,  to  deliver  to  the 
piston,  by  means  of  a  variable  steam-pipe  opening,  and  at  each 
instant  of  each  stroke,  until  cut  off  takes  place,  a  pressure  of 
steam  due  to  the  work  being  done  at  the  instant,  the  point  of 
cut-off  being  invariable. 

Whatever  quantity  of  steam,  more  or  less,  is  thus  delivered 
to  the  piston  before  cut-off  takes  place,  is  used  expansively  after 
that  point. 

The  essential  idea  of  the  cut-off  governor  is,  to  cut  off  the 
steam  supply,  which  is  of  constant  pressure,  coming  through  an 
unvaried  steam  pipe  opening,  at  such  a  point  in  each  stroke 
that  the  total  work  of  the  steam  for  that  stroke  shall  be  equal 
to  the  resistance  to  be  overcome  during  that  stroke. 

231.  The  failing  case  of  the  cut-off  governor,  and  its  remedy. 
— A  cut-off  governor  is  considered  perfect,  according  to  its  sen- 
sitiveness, by  which  it  may  cut  off  at  one-eighth,  perhaps,  of  the 
stroke,  or  not  at  all.      Now  suppose  the  case  of  frequent,  sud- 
den, and  great  changes  of  load,  as  in  a  rolling-mill.    In  driving 
the  empty  rolls,  it  may  therefore  happen  not  very  seldom  that  a 
piece  of  iron  may  be  fed  to  the  rolls,  just  after  an  early  cut-off 
has  taken  place.    In  this  case,  the  governor  was  a  false  prophet, 
not   knowing  the   future   beyond  the  point   of    cut-off,   but, 
nevertheless,  it  must  abide  by  its  own  doings,  and  no  more 
steam  can  be  had  to  do  the  work  required,  till  the  beginning  of 


300  ELEMENTS    OF 

the  next  stroke.  But  the  difficulty  is  not  necessarily  a  serious  one, 
there  being  at  least  two  remedies.  First,  to  give  out  the  steam 
power  by  quick  strokes  of  a  small  cylinder,  instead  of  slow  strokes 
of  a  great  one,  so  that  the  time  before  the  steam  will  be  ready  to 
meet  its  work  will  be  very  short.  Second,  to  provide  a  fly 
wheel,  so  heavy  that  its  inertia  will  maintain  a  nearly  uniform 
speed  during  the  remainder  of  a  single  stroke. 

232.  With  the  throttle  governor,  the  fixed  cut-off  occurs  so 
late,  comparatively,  that  there  is  a  much  smaller  chance  that 
the  foregoing  conditions  will  happen  ;  so  that  a  good  throttle  go- 
vernor, placed  directly  on  the  steam  valve  chest,  so  as  to  quickly 
deliver  to  the  piston  the  proper  pressure,  is  an  excellent  reg- 
ulator. 

Without  further  general  explanations,  we  will  proceed  to  de- 
scribe several  governors ;  chosen  from  among  a  series  of  them, 
only  with  reference  to  having  them  as  different  from  each  other 
as  possible,  and  each  the  best  of  its  class,  so  far  as  could  be  as- 
certained, having  reference  also  to  novelty.  If  space  allowed, 
it  would  have  been  interesting  to  have  illustrated  the  Sickel's 
and  other  marine  cut-offs ;  the  Corliss  and  the  Greene  (of  Pro- 
vidence, R.  I.)  variable  cut-offs,  and  the  Judson,  Tremper,  and 
Snow  throttle  governors. 


EXAMPLE  LXL 

Chul>buck'!s  Fan  Throttle  Governor. 

Description. — Not  many  fan  governors  are  made.  This  ap- 
pears strange,  in  view  of  the  apparent  simplicity  and  delicacy 
of  some  of  them,  and  the  inherent  defects  of  the  unbalanced 
ball  governor. 

PL  XXX.,  Figs.  9-13,  represent  a  very  interesting  one,  the 
figures  being  nearly  facsimiles  of  the  sketches  and  measure- 
ments taken  directly  from  a  governor  which  was  taken  apart. 
Fig.  9  is  a  side  view ;  Fig.  11  is  an  end  view,  looking  in  the 
direction  of  arrow  q  ;  and  Fig.  12,  one,  looking  in  the  direction 
of  arrow  r. 

A  is  a  section  of  the  driving  pulley.  B  the  end  of  a  f  " 
spindle,  II ;  solid  with  which  is  the  spur  wheel  II.  C  is  the  hub 
of  A,  keyed  to  I,  so  as  to  turn  the  latter.  JJ  is  a  stationary 


MACHINE   CONSTRUCTION   AND   DRAWING.  301 

?,  held  by  the  set  screw  c,  in  the  standard  KD.  The  barrel, 
E,  contains  a  coiled  spring ;  one  end  fast  to  the  inner  surface 
of  E,  the  other,  to  the  sleeve  P,  solid  with  the  sector  GGF,  and 
rotating  on  sleeve  JJ.  Fixed  to  G,  is  the  stationary  spindle,  oo, 
on  which  the  spur  wheel  M  revolves  loosely.  The  spindle,  00, 
also  carries  the  fan,  not  shown,  whose  arms  are  fixed  to  a  sleeve, 
&,  sliding  over  oo,  and  solid  with  M.  The  fan  carries  four 
skimmer-formed  vanes,  6^  inches  diameter,  and  whose  centres 
are  7  inches,  from  that  of  oo,  Fig.  13. 

The  geared  sector,  G,  actuates  the  sector  m,  which  carries  the 
spindle  n  of  the  wing  valve,  W,  seated  on  the  seat  j?.  The  open* 
ing  at  K,  covered  by  the  cap,  Q,  Fig.  10,  affords  access  to  the  valve, 
W ;  which,  when  fully  closed,  comes  edgewise  against  the  stud 
or  stop,  t,  Fig.  12.  At  L,  steam  enters  from  the  boiler,  and 
passes  through  the  valve,  and  around  its  seat,  which  forms  a 
partial  partition  within  K ;  and  passes  out  at  the  opposite  open- 
ing, R,  to  the  engine. 

The  parts  on  the  valve  spindle,  n,  are  of  brass.  The  others 
are  iron. 

The  operation  of  this  governor  is  as  follows  :  The  barrel  E, 
is  held  to  the  sleeve,  J,  by  a  set  screw.  It  can  therefore  be 
turned,  to  coil  the  spring  to  any  degree  of  tension.  The  spring 
is  also  fastened  to  the  sleeve  P,  carried  by  the  sector,  G,  so  that 
it  tends  to  hold  the  valve  W  wide  open,  and  the  more  forcibly 
so,  the  tighter  it  is  coiled. 

On  the  other  hand,  if  M  were  solid  with  G,  its  connection 
with  II  would  cause  G  to  revolve  about  B  as  a  centre.  Hence, 
just  in  proportion  as  M  resists  rotation,  does  each  successive 
radius  of  it  act  as  a  rigid  arm,  attached  to  G,  on  which  II  acts 
to  revolve  G  about  the  centre  B ;  while,  when  M  turns  with 
perfect  freedom  on  oo,  no  motion  is  imparted  to  G.  Now  see 
what  takes  place  in  practice.  If,  by  throwing  off  a  part  of  the  load 
of  the  engine,  its  speed  is  increased,  the  wheels  A,  II,  M,  and 
thence  the  fans,  will  revolve  faster ;  and  the  resistance  of  the 
air  to  the  increased  velocity  of  the  vanes  will  make  M  act  as 
described,  partially  as  if  solid  with  G,  so  that  G  will  turn  ;  and 
thence,  by  turning  m,  partially  close  the  valve,  W,  until  the  di- 
minished steam  supply  reduces  the  speed. 

But  note :  If  the  engine  be  designed  to  make  a  revolutions 
a  minute,  with  a  load  L,  with  the  valve  open  to  a  certain 
amount,  the  spring  will  be  so  set  as  to  hold  the  valve  at  th  \: 


302  ELEMENTS   OF 

opening,  in  spite  of  the  vanes,  until  that  speed  is  attained.  If 
then  the  speed  be  increased,  as  supposed,  the  resistance  of  the 
vanes  will  be  sufficient  to  overcome  the  tendency  of  the  spring 
to  keep  the  valve  open,  and  it  will  be  partly  closed.  But  tfo 
speed  can  not  thus  be  permanently  reduced  to  its  former  rate, 
for  at  that  rate,  the  valve  must  be  open  a  certain  amount,  by 
reason  of  the  mutual  adjustment  of  the  spring,  and  fan,  and 
valve.  To  run  at  exactly  the  same  speed  with  a  less  load,  the 
boiler  pressure  must  be  reduced,  or  the  hand  valve  in  the  steam 
pipe  must  be  partly  closed,  or  the  spring  must  be  relaxed,  so 
that  the  fans  will  hold  the  valve  at  a  given  opening  with  less 
resistant  effort. 

Construction.— The  three  figures  should  be  placed  side  by 
side,  with  B,  B,  B,  on  the  same  horizontal  line ;  Fig.  11,  to  the 
left,  and  Fig.  12  to  the  right  of  Fig.  9. 

Proper  scales  would  be  from  one-half  to  one-fifth  of  the  full 


EXAMPLE  LXIL 
The  Huntoon  Oil  Throttle  Governor. 

—See  PI.   XI.,  Fig.   3   and  Fig.   110.      Like 


MACHINE   CONSTRUCTION   AND   DRAWING.  303 

letters  refer  to  like  parts.  A  is  a  cylindrical  reservoir  of  oil, 
within  which  works  a  small  common  screw  propeller  B,  whose 
axis,  C,  slides  freely  in  its  bearings  DD.  A  long  pinion,  E, 
is  keyed  to  this  axis,  so  as  always  to  be  in  gear  with  its 
driver,  F,  which  is  of  greater  diameter.  F  is  fast  to  the  axis 
of  the  driving  pulley,  G,  which  is  driven  by  a  belt.  H  is  a 
lever,  actuated  by  the  moving  axis  C,  and  keyed  to  the  axis 
JK,  at  one  end  of  which  is  the  lever  KL,  weighted  with  the 
movable  weight,  M.  From  J  proceeds  the  succession  of  levers 
J]S",  and  OP,  and  their  connecting  link,  NO  ;  by  which  the 
axis,  QR,  of  the  cylindrical  valve,  SS,  is  oscillated  within  its 
concentric  seat  in  the  case,  UU,  into  which  steam  enters  at  R, 
and  leaves  at  Y,  for  the  steam  chest  on  which  the  governor 
should  stand. 

Action. — Suppose  an  engine  is  to  act  at  a  certain  speed, 
under  a  certain  average  load.  First,  suppose  that  load  uniform. 
Then  a  definite  aggregate  opening  of  all  the  rectangular  ports, 
whose  sections  appear  in  T,  will  be  required,  to  which  a  certain 
position  of  the  lever,  KL,  corresponds. 

Now,  as  the  engine  is  brought  to  the  required  speed,  we  find 
experimentally  the  position  on  the  lever  of  the  weight  M,  in 
order  that  it  shall  be  sustained  by  the  action  of  the  propeller, 
whose  operation  is  as  follows.  As  the  propeller  works  in  the 
oil  reservoir,  it  strives  to  propel  the  oil  towards  the  end  D,  of 
the  reservoir.  There  being  no  free  escape  for  the  oil,  its  reac- 
tion drives  the  propeller  and  its  axis  towards  II,  and  thus  shifts 
the  lever  II,  and  raises  KL,  which  turns  the  valve  SS  till  the 
required  opening  is  obtained. 

Second.  Suppose  the  load,  or  the  steam  pressure,  variable.  A 
momentary  increase  of  velocity  of  the  engine,  under  decrease 
of  load  or  increase  of  pressure,  will  instantly  produce  any  reas- 
onable required  increase  of  velocity  in  the  propeller,  b}7  means 
of  suitable  proportions  between  G  and  the  wheel  which  drives 
it,  and  between  F  and  E.  Then,  as  the  resistance  of  fluids  to 
motion  through  them  is  as  the  square  of  the  velocity,  or  more, 
perhaps,  the  reaction  against  a  slight  increase  in  the  velocity  of 
B  will  instantly  raise  KL,  and  close  the  openings  in  T.  The 
contrary  effect  will  result  from  a  sudden  increase  of  load 
or  a  decrease  of  pressure.  If  the  load  is  to  continue  for  some 
time,  more  or  less  than  before,  the  weight  M  must  be  shifted 
till,  at  the  same  speed  as  before,  the  valve  opening  shall  be  more 


304  ELEMENTS    OF 

or  less  also,  to  the  extent  required.  And  as  the  lever  is  moved 
but  a  very  short  distance  to  close  ftie  ports  T,  its  angular  move- 
ment, as  indicated  by  the  difference  of  length  of  F  and  E,  is  so 
small  for  any  given  average  load  and  speed,  that  it  is  raised 
with  practically  equal  facility  through  all  points  of  its  small 
motion. 

Finally,  when,  in  case  of  a  nearly  uniform  load  and  pressure, 
the  weight  M  need  not  be  shifted,  it  is  hung  by  a  chain  wrap- 
ping on  a  curved  sector,  of  which  KL  is  the  arm  or  spoke.  It 
will  then  rise  and  fall  vertically. 

Construction. — No  measurements  have  been  placed  on  the 
figures,  since  the  governor  is  made  of  various  sizes.  If  the 
diameter  of  B  be  taken  at  7-J-  inches,  it  may  serve  as  a  scale  for 
the  construction,  and  PI.  XI.,  Fig.  3,  will  afford  all  the  data 
essential  for  transforming  Fig.  110  into  plans,  elevations,  and 
sections. 

EXAMPLE  LXIII. 

ight^s  Variable  Cut-off  by  the  Governor. 


Description. — See  Fig.  Ill,  giving  a  general  view  of  the 
front  portion  of  the  engine,  and  Fl.  XXXI.,  Figs.  6-10,  show- 
ing the  governor,  with  plan  enlarged.  Fig.  8  is  a  smaller  plan 
view,  showing  the  valve-stems  and  their  heads. 

The  engine,  to  which  this  governor  is  attached,  has  a  variable 
cut-off,  and  its  connections  with  the  governor  are  such,  that  the 
point  of  cutting  off  steam  is  made  automatically  variable  to  suit 
the  requirements  of  the  machinery  driven  by  the  engine,  there- 
by measuring  out  just  the  amount  of  steam  necessary  to  meet 
any  variations  in  the  power  required,  which  are  constantly 
occurring  in  all  engines  used  for  manufacturing  purposes.  The 
induction  valves,  which  are  of  the  balance  poppet  kind,  are 
arranged  in  separate  chests,  II,  Fig.  Ill,  on  the  side  of  the 
cylinder,  having  a  steam  connection  with  the  pipe  cast  with  the 
cylinder.  The  engine  has  independent  exhaiist  valves  in  the 
bottom  of  the  cylinder,  which  are  brought  as  close  as  practicable 
to  the  end  of  the  cylinder  to  obviate  waste  of  steam  in  filling 
the  passages.  These  are  slide-valves,  worked  by  a  rod  taking 
hold  of  the  valve  from  the  underside,  the  rod  being  in  the 
exhaust  steam,  thereby  obviating  the  necessity  of  stuffiiur-boxes 


MACHINE   CONSTRUCTION    AND   DRAWING. 


305 


in  the  live  steam,  and  they  are  worked  with  the  minimum 
amount  of  friction.  The  maximum  pressure  on  these  valves  is 
at  the  ends  of  the  stroke,  and  they  are  relieved  of  the  pressure 


Fia.  111. 


in  proportion  to  the  expansion  of  the  steam  in  the  cylinder  dur- 
ing the  stroke. 

It  may  be  the  case  with  this  class  of  engines,  when  used  for 
20 


306  ELEMENTS   OF 

manufacturing  purposes,  that  when  they  are  working  with  a 
minimum  amount  of  power,  the  cut-off  takes  place  so  early  in 
the  stroke  as  to  reduce  the  pressure  of  steam  down  to  the  atmo- 
sphere before  the  stroke  is  completed.  This  involves  a  loss  of 
power  during  the  balance  of  the  stroke  by  producing  a  partial 
vacuum  on  the  steam  side  of  the  piston  ;  but  by  giving  a  due 
lead  to  the  exhaust,  the  valves  prevent  this  vacuum,  and  the 
consequent  loss  of  power ;  which  result  cannot  be  produced 
without  an  independent  exhaust. 

Indeed,  engines  generally,  with  variable  cut-offs,  have  inde- 
pendent exhaust-valves,  as  in  the  Corliss,  Greene,  and  Putnam 
engines. 

Both  the  eduction  and  induction  valves  are  worked  from  a 
horizontal  shaft,  parallel  to  the  cylinder,  and  driven  by  spur  and 
bevel  gearing  from  the  crank  shaft.  Cranks  on  this  parallel 
shaft  actuate  the  exhaust  valves  transversely  to  the  cylinder. 
The  induction  valves  are  opened  in  the  direction  of  the  arrows 
by  a  cam,  F,  on  a  hollow  upright  shaft,  K,  arranged  in  suitable 
fixed  bearings  between  the  heads,  A,A,  of  the  two  valve-stems, 
d,d.  See  also  Fig.  8.  The  valves  are  closed  to  produce  the 
cutting-off  of  the  steam,  by  springs  or  by  the  pressure  of  the 
steam  on  the  ends  of  their  stems.  The  cam  shaft,  K,  has  a 
bevel  gear  at  the  bottom,  through  which  it  is  driven  by  a  bevel 
gear,  (r,  on  a  horizontal  shaft,  H,  which  is  arranged  alongside 
the  cylinder,  and  which  derives  motion  through  bevel  gearing 
from  the  main  shaft  first  mentioned.  Fig.  7  shows  a  side  eleva- 
tion of  the  gear  and  cam  boxes  S  and  R. 

The  cam,  F,  is  constructed  with  two  pairs  of  sliding  toes,  t,t', 
.and /",/"',  one  pair  for  operating  each  valve,  and  as  one  of  the 
toes  for  each  valve  operates  during  every  half  revolution  of  the 
shaft,  K,  the  said  shaft  only  makes  one  revolution  for  every  tivo 
revolutions  of  the  crank  shaft..  The  toes  are  cogged  on  their 
inner  edges,  as  shown  in  plan,  to  gear  with  long  straight  cogs, 
n,  on  a  spindle,  N^N^N",  which  passes  through  the  hollow  main 
spindle,  MM',  of  the  governor,  and  which  is  so  suspended  from 
the  governor  at  O  as  to  be  raised  and  lowered  as  the  balls  of 
the  governor  rise  and  fall.  This  spindle,  N,  has  on  its  lower 
part  a  series  of  spiral  cogs  or  threads,  r,  which  fit  and  work  like 
a  many4hreaded  screw  in  a  nut,  P,  formed  or  screwed  within 
the  lower  part  of  the  cam-shaft.  The  Governor  is  driven  by 
bevel  gear,  m,m'  and  #,<?•>  on  tne  upper  end  of  the  shaft,  K. 


MACHINE   CONSTRUCTION  AND  DRAWING.  307 

The  spindle,  !N",  rotates  with  the  cam-shaft,  and  always  rotates 
at  the  same  velocity,  so  long  as  the  speed  of  the  engine  and 
governor  is  invariable  ;  but,  whenever  the  speed  of  the  engine 
varies,  and  causes  a  variation  in  the  plane  of  revolution  of  the 
Governor  balls,  the  spindle,  Is",  rises  or  falls,  and  in  so  doing  is 
caused  to  turn  independently  of  the  cam-shaft  by  the  longitu- 
dinal movement  of  the  spiral  cogs  or  threads,  r,  in  the  nut  within 
the  lower  end  of  the  said  shaft.  By  that  means,  the  said  spin- 
dle is  caused  to  turn  within  the  cam-shaft,  and  in  this  way  the 
straight  cogs,  n,  on  the  said  spindle,  are  made  to  act  upon  the 
cogs  of  the  toes,  tt',  of  the  cut-off  cam,  and  thereby  to  produce 
a  greater  or  less  opening  of  the  induction  valves,  and  to  expe- 
dite or  retard  the  closing  or  cutting-off  movement,  according  to 
the  requirements  of  the  engine. 

The  toes  are  ribbed  on  their  upper  and  under  sides  as  seen 
at  t'.  These  ribs  guide  the  toes  in  and  out,  horizontally,  in  the 
grooves  aa  and  Hb.  See  the  arrows  in  the  plan. 

Thus,  the  farther  out  the  toes  are  thrown,  by  the  rotation  of 
the  long  pinion,  consequent  on  the  falling  of  the  balls  and  the 
spindle,  1ST,  with  the  screw,  rr,  the  wider  will  the  valves  be 
opened,  and  the  longer  they  will  stay  open. 

Construction. — By  placing  the  figure  lengthwise  of  the  plate, 
or  by  making  it  on  a  folding  plate  it  may  be  made  on  a  scale 
of  from  three-eighths  to  jit 


EXAMPLE  LXIV. 
Bcibcock  and  Wilcox  Governor  and  Variable  Cut-off. 

Description. — With  this  remarkable  example  of  the  present 
group,  there  are  coupled,  by  way  of  a  summary  of  information, 
various  points  concerning  steam  engines  ;  collected  from  de- 
scriptive articles  in  several  scientific  periodicals. 

Most  of  the  features  of  modern  steam  engineering  originated 
in  the  fertile  brain  of  James  Watt.  He  found  the  steam  engine 
in  a  very  crude  state,  and  left  it  in  quite  as  perfect  a  condition 
(e  ccepting  only  mechanical  construction)  as  that  of  the  ordinary 
engines  at  the  present  time.  He  invented  separate  condensa- 
tion, expansion,  steam  jacketing,  superheating,  and  the  gover- 
nor. The  combination  of  the  governor  with  a  cut-off  valve 


308  ELEMENTS   OF 

gear,  was  reserved  to  a  later  period,  having  first  been  published 
in  the  "Repertory  of  Patent  Inventions"  for  1826,  as  the  in- 
vention of  James  Whitelaw.  Since  then  the  steam  engine  has 
advanced  by  improvement  in  details  and  construction,  rather 
than  by  the  development  of  new  principles. 

The  engine  herewith  partly  presented  makes  no  pretension 
to  radical  improvements  in  the  principle  of  using  steam  expan- 
sively, but  it  embraces  a  novel,  simple,  and  highly  effective  me- 
thod of  operating  and  controlling  the  action  of  the  valves  for 
admitting  and  cutting  off  the  steam. 

There  is  no  necessity  at  the  present  day  to  argue  the  superior- 
ity of  an  engine  regulated  by  a  good  cut-off,  so  far  as  economy 
of  fuel  or  regularity  of  speed  are  concerned. 

This  engine  has  a  novel  construction  of  the  governor,  by 
which  the  variation  (228)  due  to  the  pendulum  action  of  the 
ordinary  governor  is  overcome,  and  a  regulator  produced,  which 
will  give  the  same  speed  whether  the  engine  be  lightly  or  heavily 
loaded,  or  the  pressure  of  steam  in  the  boiler  be  greater  or  less. 
The  governor,  as  invented  by  "Watt,  and  adopted  by  modern 
engineers  with  rare  exceptions,  gives  only  an  approximation  to 
equal  speed,  requiring  a  variation  of  from  five  to  thirty  per 
cent,  between  the  extremes  of  motion.  This  we  have  seen. 

In  designing  this  engine,  it  has  been  the  object  not  only  to 
introduce  peculiar  ideas  and  improvements,  but  to  combine 
therewith  all  those  features  which  long  practice  has  proved  to 
be  most  conducive  to  economy  of  fuel,  and  the  durability  of  all 
the  working  parts.  The  steam  jacket  has  been  much  neglected 
in  this  country,  though  in  almost  universal  use  by  the  best  en- 
gine makers  of  Europe ;  and  so  little  are  its  theory  and  advan- 
tages understood  here,  that  often  where  it  has  been  introduced 
in  this  country  it  is  filled  with  the  exhaust  steam,  thus  partly 
defeating  the  very  object  for  which  it  was  designed.  This  en- 
gine is  jacketed  with  live  steam  from  the  boiler,  in  both  heads, 
as  well  as  around  the  cylinders,  thereby  keeping  the  metal  of 
the  cylinders  as  hot  as  the  hottest  steam  which  enters  it. 

The  valves  which  affect  the  distribution  of  the  steam  in  the 
steam  engine,  are  the  most  important  part  of  the;  machine,  as 
upon  their  properly  performing  their  functions  depends  the 
efficiency  of  the  engine.  They  must  not  only  admit,  exhaust, 
shut  off,  and  close,  at  the  proper  periods,  but  they  must  be  per- 
fectly tight  when  closed;  and,  when  open,  admit  the  steam 


MACHINE   CONSTRUCTION   AND  DRAWING.  309 

with  the  least  possible  resistance.  They  should  also  permit  of 
such  a  relation  to  the  cylinder  as  to  give  the  least  practicable 
lost  space  or  clearance.  There  are  four  distinct  varieties  of 
valves  used  for  this  purpose,  viz. :  the  plug  or  cock,  the  piston, 
the  seat  valve  or  poppet,  and  the  slide.  The  first  variety  is 
never  used  now  by  competent  engineers,  having  but  one  good 
quality,  viz. :  the  equal  pressure  of  steam  on  its  sides,  to  balance 
its  many  bad  features,  such  as  leakages,  sticking  from  expan- 
sion, and  unequal  wear.  The  piston  valve  is  also  nearly  out  of 
use  owing  to  the  lost  space  inherent  in  its  construction.  The 
same  objection  applies  to  the  poppet  valve,  with  the  additional 
ones  of  great  liability  to  leakage  and  inability  to  open  and  close 
quickly,  from  the  fact  that  it  opens  immediately  on  starting, 
and  is  not  closed  until  brought  to  rest.  It  is  impossible  to  start 
or  stop  the  valve  instantaneously ;  therefore  the  opening  and 
closing  must  be  correspondingly  so  slow  as  to  be  objectionable 
except  on  slow  moving  engines. 

The  universal  experience  in  this  country  and  in  Europe,  is  in 
favor  of  the  slide  valve  for  opening  and  closing  the  ports  of  all 
quick  moving  engines.  It  is  simple  and  easily  fitted,  admits  of 
the  least  lost  space,  opens  and  closes  the  ports  with  the  quickest 
possible  motion,  and  is  the  least  liable  to  become  leaky  from 
use  of  any  form  of  valve.  Of  the  two  forms  of  slide  valve  the 
flat  is  preferable  to  the  curved,  from  the  greater  facility  of  ac- 
curate fitting,  and  the  more  equal  wear  of  two  planes  as  com- 
pared to  inner  and  outer  cylindrical  surfaces. 

An  important  condition  of  equal  wear  in  a  slide  valve,  how- 
ever, is  a  constant  travel.  "Where  the  induction  valve  is  made 
also  to  act  as  a  cut-off  valve,  as  in  a  link  motion,  this  condition 
cannot  obtain,  and  as  a  consequence  we  find  that  such  valves 
are  more  apt  to  leak. 

The  adaptation  of  a  cut-off  mechanism,  to  act  in  conjunction 
with  a  plain  slide  valve,  the  latter  to  admit  and  exhaust  the 
steam,  and  the  former  to  close  the  port  at  any  desired  point  in 
the  stroke,  has  been  a  favorite  pursuit  of  engineers  for  the  past 
half  century.  Nine-tenths  of  all  the  expansion  engines  now 
built  in  Europe  have  some  modification  of  this  form  of  valve 
gear,  and  the  engine  of  Messrs.  Farcot  &  Sons,  which  received 
the  Grand  Prize  at  the  late  Paris  Exposition,  was  of  this  class. 

One  of  the  points  in  which  the  Babcock  &  Wilcox  engine 
differs  from  those  which  have  preceded  it,  is  the  manner  in 


310  ELEMENTS   OF 

which  the  cut-off  valves  are  operated,  viz. :  by  the  action  of  the 
steam  itself,  independent  entirely  of  the  action  of  the  main 
valve  ;  thus  insuring  an  instantaneous,  positive,  and  easily  con- 
trolled cut-off,  at  any  desired  point  in  the  stroke  of  the  piston. 
The  distribution  of  the  steam  to  the  alternate  sides  of  the  pis- 
ton, and  its  release  from  the  cylinder  when  the  stroke  is  com- 
pleted, are  performed  in  the  manner  most  approved  by  expe- 
rienced engineers,  by  means  of  a  plain  slide  valve  operated  by 
the  ordinary  eccentric.  But  from  the  fact  that  the  induction 
valve  has  in  no  case  to  act  as  a  cut-off  valve,  and  from  the 
further  fact  that  the  cut-off  is  actuated  independently  of  the 
motion  of  the  main  valve,  the  functions  of  "  lead  "  and  "  cushion  " 
can  be  adjusted  to  any  desired  degree,  without  in  any  manner 
affecting  the  action  of  the  cut-off  valve.  This  is  an  important 
distinction  between  the  operation  of  the  main  valve  of  this  en- 
gine, and  of  those  which  have  preceded  it.  In  the  ordinary 
three-ported  slide  valve,  or  in  any  other  arrangement  where  the 
several  functions  of  lead,  cut- off,  release,  and  compression,  or 
closing  the  exhaust,  are  dependent  on  the  motion  of  one  eccen- 
tric, the  "  exhaust "  functions — i.  e.,  the  release  and  compres- 
sion— must  always  be  subservient  to  the  "  steam  "  functions — i. 
e.,  the  lead  and  suppression,  or  cut-off.  The  cut-off  mechanism 
consists  of  two  cut-off  slides,  a  miniature  steam  cylinder,  and  a 
valve  for  controlling  the  admission  of  steam  to  the  same.  This 
small  cylinder,  being  enveloped  in  the  steam,  requiring  no 
packing,  and  having  only  the  weight  of  its  piston  to  produce 
wear,  is,  for  all  practical  purposes,  indestructible.  The  cut-off 
slides  are  always  balanced  when  they  move,  consequently  they 
are  not  exposed  to  injurious  wear. 

The  bed  or  framing  which  has  been  adopted  for  the  horizon- 
tal engines  is  of  the  form  first  introduced  by  Horatio  Allen,  of 
the  K" ovelty  Iron  Works,  New  York.  It  is  bolted  to  the  end  of 
the  cylinder,  and  extends  to  the  pillow-block,  and  the  metal  is 
so  disposed  as  to  give  the  greatest  rigidity  with  the  least  weight. 
The  cross-head  is  upright,  and  is  supported  on  flat  slides,  a  drip 
cup  cast  on  the  bed  serving  to  catch  all  drippings,  not  only 
from  the  slides,  but  from  all  the  stuffing  boxes. 

The  regulator  or  governor  is  driven  by  gearing,  thus  avoiding 
all  danger  of  breakage  or  slipping  of  belts,  and  the  consequent 
damage  to  the  engine  and  machinery  from  the  "running  away" 
of  the  engine. 


MACHINE   CONSTRUCTION  AND   DRAWING.  311 

In  addition  to  the  steam  jacket  for  preserving  the  tempera- 
ture of  the  cylinder,  a  covering  of  felt  is  employed  around  all 
the  exposed  parts,  and  this  in  turn  is  covered  by  a  casing  of 
polished  metal.  The  latter  is  the  best  possible  protection 
against  loss  by  radiation. 

PI.  XXXII.,  Fig.  1,  represents  a  horizontal  section  of  the 
cylinder  and  valves,  on  X'X'  and  YY',  Fig.  2,  showing  the 
peculiarities  of  the  cut-off  motion.  A  is  a  cylinder,  which  is 
steam  jacketed,  as  are  also  the  heads,  at  aa.  B  is  a  portion  of 
the  bed  piece,  which  forms  also  the  front  head  of  the  cylinder. 
C  is  the  piston,  and  C'  the  piston  rod.  D  is  the  main  valve, 
ee  the  induction  ports,  and  F  is  the  exhaust  port.  The  body 
of  the  valve  is  hollow,  and  conveys  the  exhaust  steam,  from 
either  end  of  the  cylinder,  alternately,  to  the  exhaust  port,  F, 
•whence  it  goes  into  the  exhaust  pipe.  The  steam  passes  through 
ports  e'  in  each  end  of  the  valve,  into  the  induction  ports  of  the 
cylinder,  alternately,  as  they  are  opened  by  the  motion  of  the 
valve  derived  from  an  eccentric  in  the  usual  manner.  On  the 
back  of  the  valve,  at  each  end,  is  a  slide,  G,  which  can  be  made 
to  cover  the  port  at  that  end,  and  these  slides  are  attached  to  a 
piston  H,  fitting  in  a  small  steam  cylinder  bolted  to  the  back 
of  the  valve,  and  so  adjusted  so  that  when  the  port  in  one  end 
of  the  valve  is  closed  the  other  is  open.  Upon  steam  being  ad- 
mitted to  either  end  of  the  piston  H,  the  piston  is  shot  over, 
and  the  corresponding  slide  closed,  to  cut  off  steam  from  that 
end  of  the  main  cylinder ;  while  the  port  at  the  other  end  of 
the  main  valve  is  opened  ready  to  admit  steam  to  the  other  side 
of  the  main  piston  when  the  valve  shall  arrive  at  the  proper 
position. 

It  will  be  observed  that  the  cut-off  slides,  G,  are  always  bal- 
anced when  moved.  The  one  about  to  close  having  steam  of 
equal  pressure  upon  each  side ;  while  the  other  one  has  been 
balanced  by  the  main  valve  riding  past  the  end  of  the  valve 
face  on  the  cylinder,  thus  admitting  steam  behind  the  slide,  G. 
This  condition  obtains  during  the  whole  stroke  of  the  piston 
until  the  steam  is  cut  off,  after  which  the  cut-off  slides  G,  re- 
main stationary  relatively  to  the  main  valve  until  ready  to  cut 
off  steam  on  the  return  stroke,  previously  to  which  they  have 
been  balanced  by  the  over-riding  of  the  valve  at  the  other  end 
These  slides  experience,  therefore,  almost  no  wear,  and,  once  fit- 
ted tight,  they  will  remain  so  indefinitely.  The  piston  H,  in  tlie 


312  ELEMENTS   OP 

small  cylinder,  is  turned  to  fit,  and  has  no  packing,  neither  have 
the  rods  stuffing  boxes,  as  the  pressure  is  equal  on  both  sides, 
except  during  the  inappreciable  time  which  intervenes  between 
the  exhausting  of  the  cylinder,  I,  and  the  movement  of  the 
piston.  The  only  tendency  to  wear  in  these  parts  is  due  to  the 
weight  of  the  piston  and  rods,  which  are  supported  on  large 
surfaces.  In  fact,  after  twenty  months  constant  use,  none  of 
these  parts  have  worn  sufficiently  to  obliterate  the  tool  marks 
upon  the  surfaces. 

Steam  is  admitted  alternately  to  each  end  of  the  piston,  H, 
at  every  revolution  of  the  engine,  causing  the  cut-off  slides  to 
move  at  every  stroke,  cutting  off  the  steam  at  the  point  deter- 
mined by  the  governor. 

Fig.  2  shows  a  cross  section  on  XX.  The  valve,  J,  V  of  the 
cylinder,  HH',  is  balanced  by  the  plate,  J,  upon  its  back,  and  is 
operated  by  a  toe,  £,  upon  the  rock  shaft,  L,  carried  upon  the 
main  valve,  and  extending  through  the  end  of  the  steam  chest 
where  it  receives  motion  from  a  crank,  m,  on  a  shaft,  n,  which 
is  oscillated  by  the  governor.  The  exhaust  ports,  f,  of  the 
cylinder,  I,  are  made  upon  the  bottom,  and  are  at  a  little  dis- 
tance from  the  end,  while  the  steam  ports,  <7,  are  upon  the  side 
and  at  the  extreme  end  of  the  cylinder.  By  this  arrangement 
the  piston  closes  its  own  exhaust  port,  and  cushions  on  the  re- 
maining distance,  thus  dispensing  with  all  dash-pots  or  air  cush- 
ions, and  causing  the  valve  to  move  without  any  noise. 

The  valve,  J,  being  balanced,  and  the  rod,  L,  carried  through 
its  stuffing  box  by  the  main  valve,  there  is  the  least  possible  power 
required  by  the  regulator  to  adjust  the  crank,  m,  thereby  ensur- 
ing more  sensitive  action  than  can  be  attained  where  the  gov- 
ernor has  labor  to  perform. 

The  governor  is  peculiar,  and  is  shown  at  Fig.  112.  The 
balls,  N",  are  hung  upon  arms  in  the  usual  manner,  which  arms 
are  jointed  at  their  upper  ends  to  a  head  attached  to  the  rod,  o, 
which  slides  within  the  hollow  shaft,  &,  that  drives  the  balls  ; 
the  motion  being  communicated  through  the  radius  rods,^>, 
which  are  jointed  at  their  lower  ends  to  the  gearing  shaft,  and  at 
their  upper  ends  to  the  centre  of  the  arms,  n.  The  rods,  p,  are 
half  the  length  of  the  arms,  n,  measuring  from  the  centre  of  the 
ball,  and  it  will  be  readily  seen  that,  in  consequence  of  this 
arrangement,  the  arms,  n,  and  rods,  p,  form  a  parallel  motion, 
and  compel  the  balls  to  move  outward  in  a  horizontal  plane. 


MACHINE   CONSTRUCTION   AND   DRAWING.  313 

In  the  ordinary  pendulum  governor,  the  balls  move  in  the 
arc  of  a  circle,  and  rise  as  they  extend.  It  therefore  requires 
an  increased  speed  to  maintain  them  in  their  advanced  position. 
The  engine  must  consequently  run  faster  when  the  load  is  light 
than  when  it  is  heavy,  and  such  is  the  case  with  all  ordinary 
governors  (228).  In  this  improved  governor,  it  will  be  seen 
that  the  gravity  of  the  balls  has  no  tendency  to  move  them  in 
either  direction,  and  exerts  no  influence  whatever  upon  the 
speed  of  the  engine.  The  centrifugal  force  causes  them  to  di- 
verge, and  a  weight,  "W,  tends  to  bring  them  towards  the  shaft. 
"When,  therefore,  these  two  forces  are  in  equilibrium,  the  balls 
will  remain  in  the  same  position ;  but,  as  either  preponderates,  they 
are  moved  in  a  corresponding  manner,  thus  affecting  the  speed 
of  the  engine  by  varying  the  amount  of  cut-off.  The  weight, 
TV,  is  supported  upon  a  bent  lever,  I,  which  is  so  proportioned, 
that  the  centrifugal  force,  at  any  given  speed,  will  just  balance 
the  weight  in  all  positions.  The  speed  of  the  engine  will, 
therefore,  remain  at  that  fixed  point  with  all  variations  of  load 
or  pressure  of  steam  ;  for  any  increase  or  diminution  will  cause 
either  the  balls  or  weight  to  preponderate,  and  the  point  of  cut- 
off to  be  changed,  until  the  speed  is  again  brought  to  the 
standard  where  the  two  forces  are  in  equilibrium. 

Any  desired  speed  for  a  given  load,  can  be  obtained  by 
altering  the  weight,  W,  and  the  action  of  the  governor  will 
be  as  perfect  in  one  case  as  in  any  other.  A  spiral  on  the  rod, 
o,  serves  to  advance  or  retire  the  crank,  m,  relatively  to  the 
main  crank,  so  as  to  cause  the  cut-off  to  occur  earlier  or  later  in 
the  stroke,  as  the  balls  diverge  or  converge  ;  and  the  amount  of 
this  adjustment  is  such  that  the  cut-off  may  be  varied  from 
one  eighth,  of  the  stroke,  to  the  end  of  the  stroke. 

The  Balanced  Governor  is  a  radical  improvement.  The 
vices  of  the  old  governor  are,  that  the  extension  of  the  revolv- 
ing balls  (by  which  the  steam  supply  is  shortened  or  lengthened 
as  the  speed  is  accelerated  or  checked)  is  resisted  by  their 
weights  at  a  progressive  leverage,  and  fails  to  represent  truly 
the  changes  of  speed :  and,  secondly,  that  a  given  force  of  steam 
can  only  be  had  at  a  given  speed, — because  a  given  posi- 
tion of  the  balls  determines  a  certain  opening  of  the  governor 
valve, — whatever  the  load  may  demand,  so  that  if  the  load  is 
much  lightened  the  steam  is  shortened  only  by  running  at  a 
high  speed,  or  if  the  load  is  heavily  increased,  the  engine  must 


314 


ELEMENTS    OF 


run  slow  to  get  steam  to  meet  it — except  as  regulated  ~by  hand. 
The  balls  of  the  new  governor  have  nothing  of  the  pen- 
dulum character,  but  extend  in  a  horizontal  plane,  with  equal 
ease  at  either  extreme  of  their  oscillation,  faithfully  repre- 
senting all  the  fluctuations  of  the 
speed.  Their  centrifugal  tendency, 
at  the  speed  intended  to  be  main- 
tained, is  accurately  counterbal- 
anced by  a  weight,  drawing  them 
inward  with  a  progress! ve  leverage 
responding  to  every  change  in  their 
position  and  force.  The  consequence 
is  that  so  long  as  the  prescribed  speed 
is  maintained,  the  position  of  the 
balls  is  independent  of  the  speed  ; 
they  revolve  far  in  or  far  out,  indif- 
ferently, so  as  to  give  steam  accord- 
ing to  the  wants  of  the  load,  with 
one  and  the  same  speed  in  all  cases. 
If  a  change  is  made  in  the  load, 
the  speed  for  the  moment  suffers 
change,  the  equilibrium  of  forces 
in  the  balls  is  disturbed,  and  the 
preponderating  force  places  the  un- 
resisting balls  instantly  in  the  pro- 
per position  to  meet  the  new  de- 
mand for  steam ;  and  there  they 
stay  (the  speed  being  lighted  and 
equilibrium  thus  restored)  until  an- 
other change  of  load  summons  them 
to  a  new  position.  The  simple  mechanism,  by  which  the 
regulation  of  stearc  is  perfected  in  this  governor,  will  repay  a 
more  particular  examination. 

Construction. — The  student  can  profitably  make  Plate 
XXXII.  on  double  the  present  scale,  or  from  one-fourth  to  one- 
sixth  of  the  full  size. 


w 


Indicator  Diagrams. 

233.  The  only  means  we  have  of  tracing  the  action  of  the 
steam  within  the  cylinder — the  time  and  rapidity  of  its  entrance, 


MACHINE   CONSTRUCTION   AND   DRAWING.  315 

the  point  of  cut-off,  its  action  in  expanding,  the  time  of  release, 
the  amount  of  back  pressure,  compression,  etc. — is  by  diagrams 
drawn  by  an  "  Indicator," — an  instrument  actuated  by  the  pres- 
sure of  the  steam  and  the  motion  of  the  piston.  These  two 
motions,  acting  at  right  angles,  produce  a  curve  which  indicates 
the  exact  pressure  of  steam  at  each  portion  of  the  stroke  of  the 
piston,  in  and  out.  The  line  thus  drawn,  during  a  complete 
revolution  of  the  engine,  encloses  an  irregular  figure,  the  shape 
of  which  varies  with  every  different  condition  in  the  elements 
which  form  it,  and  by  it  we  are  enabled,  not  only  to  determine 
the  actual  power  exerted  by  the  steam,  but  also  the  relative  per- 
fection of  the  valve  motion,  and  the  effect  of  different  propor- 
tions between  the  piston  and  passages. 

The  importance  of  the  Indicator  as  a  means  of  studying  the 
action  of  any  given  engine,  and  of  comparing  the  relative  values 
of  different  constructions  and  proportions,  though  known  from 
the  time  of  Watt,  has  but  recently  been  fully  appreciated  by 
engineers ;  and,  in  fact,  not  until  within  a  very  few  years  has 
there  been  an  instrument  manufactured,  capable  of  being  used 
with  any  satisfactory  degree  of  accuracy  upon  the  quick  moving 
engines  now  employed  for  most  stationary  purposes.  To  its 
employment  the  world  is  indebted  for  its  most  satisfactory 
practical  knowledge  of  the  action  of  steam,  and  the  best  meana 
of  obtaining  the  highest  economical  results. 

But  in  order  to  compare  one  engine  with  another,  they  should 
be  in  precisely  similar  circumstances.  As,  however,  this  rarely 
occurs,  it  is  necessary  to  have  some  standard  by  which  all  en- 
gines may  be  compared  and  their  relative  performance  deter- 
mined. The  best  means  for  doing  this  is  to  compare  each  en- 
gine with  a  theoretically  perfect  engine  of  the  same  size  under 
the  same  circumstances. 

The  expansion  of  steam  follows  certain  laws,  and  the  quan- 
tity of  steam  being  known,  as  well  as  the  space  which  it  occu- 
pies, it  is  possible  to  tell  the  correct  pressure  for  each  variation 
in  the  space  occupied.  A  curve  can  thus  be  calculated  which 
is  of  hyperbolic  form,  and  which  will  give  a  diagram  of  the 
theoretical  action  of  a  given  amount  of  steam  in  a  given  size  of 
cylinder.  The  diagrams  taken  from  any  engine  may  thus  be 
compared  with  a  theoretical  diagram,  for  the  same  quantity  of 
steam  used  in  the  same  sized  cylinder,  and  the  ratio  existing 
between  the  actual  and  the  theoretical  diagrams  will  serve  as  a 


316  ELEMENTS   OF 

measure  of  the  perfection  of  the  engine  and  valve  mechan- 
ism. 

For  the  illustration  of  this  subject,  several  diagrams  follow, 
which  have  been  taken  from  different  engines,  with  the  theore- 
tical diagram,  for  each  case,  the  latter  allowing  for  no  losses 
from  any  source.  It  is  impossible  to  construct  an  engine  in 
which  there  shall  be  no  loss  from  friction  of  the  steam  in  the 
pipes  and  passages,  or  from  clearance. 

In  these  diagrams,  the  highest  line,  AB,  represents  the  pres- 
sure of  steam  in  the  boiler,  and,  with  the  exception  of  those 
from  condensing  engines,  the  lowest  line,  CD,  that  of  atmo- 
spheric pressure.  The  scale  marked  upon  each  diagram  is  the 
fraction  of  an  inch  which  represents  one  pound  of  steam  pres- 
sure in  the  vertical  lines  of  the  diagram.  The  horizontal  length 
of  the  diagram  represents  the  length  of  stroke  of  the  engine,  plus 
an  amount  of  space  at  the  end  (exterior  to  the  heavy  outline), 
which  is  called  the  "clearance,"  and  represents,  in  the  same 
scale  as  the  stroke,  the  amount  of  space  included  between  the 
end  of  the  cylinder  and  the  piston  at  the  extreme  of  motion  of 
the  latter,  and  also  the  contents  of  the  passage  ways.  It  will  be 
seen  that  the  length  of  stroke  is  represented  by  no  particular 
scale,  but  each  of  the  divisions  is  one-tenth  of  the  full  stroke. 
The  heavy  outline  is  the  diagram  formed  by  the  indicator,  and 
represents  truly  the  pressure  in  the  cylinder  at  each  fraction  of 
the  motion  of  the  piston.  Where  the  line  commences  to  fall 
abruptly,  as  at  F,  is  the  "  point  of  cut-off,"  and  shows  the  por- 
tion of  the  stroke  in  which  the  steam  is  admitted.  During  the 
remainder  of  the  stroke,  the  steam  expands,  reducing  the  pres- 
sure, and  forming  a  curve,  called  the  "  expansion  curve."  At, 
or  just  before,  the  end  of  the  stroke,  the  steam  is  released,  and 
"  exhaust "  commences.  The  returning  line  shows,  by  its  dis- 
tance from  the  base  line,  the  amount  of  "  back  pressure."  In  a 
properly  constructed  engine,  the  exhaust  closes  a  little  before 
the  termination  of  the  return  stroke,  thus  confining  the  remain- 
ing steam,  compressing  it,  and  forming  a  "  cushion  "  to  stop  the 
momentum  of  the  piston,  and  prepare  it  for  the  return  stroke. 
This  is  shown  by  the  rounding  of  the  corner  and  the  rising  of 
the  pressure  at  the  termination  of  the  stroke. 

The  dotted  outline  represents  the  theoretical  power  of  the 
amount  of  steam  exhausted  from  the  cylinder  in  each  instance, 
when  used  in  a  cylinder  of  the  same  size,  with  no  losses  from 


MACHINE   CONSTRUCTION   AND   DRAWING. 


317 


friction  in  the  passages,  back-pressure,  or  clearance.  The  pro- 
portion of  the  area  of  the  actual  to  the  theoretical  diagram  re- 
presents the  relative  efficiency  of  the  given  engine,  and  is  stated 
in  percentage  of  the  theoretical  efficiency  in  connection  with 
each  individual  diagram. 

Nos.  1  and  2  were  taken  from  a  12-inch  engine,  3  feet  stroke, 


making  64  revolutions.  In  No.  1  the  actual  is  89  per  cent,  of 
the  theoretical  diagram,  and  in  No.  2,  82  per  cent.  The  losses 
in  this  case  are  due  to  the  friction  of  the  steam  in  the  pipe  and 


These  cards  are  taken  from  the  first  Babcock  &  Wilcox  en- 
gine ever  built. 


318  ELEMENTS   OF 

No.  3  is  from  a  14  by  42  inch  engine.  The  engine  makes  65 
revolutions  per  minute  or  455  feet  of  piston  speed.  This  is  one 
of  a  large  number  of  equally  good  cards  taken  from  this  en- 
gine, and  the  actual  diagram  is  92£  per  cent,  of  the  theoretical. 


233.  Leaking  valves,  or  pistons,  ill  proportioned  steam  passa- 
ges, an  improper  amount  of  compression,  back  pressure  arising 
from  a  too  long,  circuitous,  or  otherwise  hindered  exhaust,  a 
general  bad  condition  of  the  engine,  or  an  overestimated  boiler 
pressure,  given  by  inaccurate  gauges,  may  all  make  an  abnor- 
mal difference  between  the  actual  power  given  out,  as  repre- 
sented by  the  indicator  diagram,  correct  as  that  may  be,  and 
any  alleged  corresponding  theoretical  diagram. 

With  these  explanations,  \vhich  the  rigorous  impartiality  of  a 
text  book  imperatively  demands,  the  following  vicious  diagrams 
are  given  in  illustration  of  them ;  and  without  implying  that 
better  ones  could  not  be  taken  from  perfect  engines  of  the  de- 
signs which  they  represent. 

Indeed,tit  is  much  to  be  desired  that  a  series  of  diagrams 
might  be  taken  from  the  best  specimens  of  all  our  best  engines, 
by  a  board  of  entirely  disinterested  experts,  and  from  each  en- 
gine by  each  of  a  number  of  indicators. 


MACHINE   CONSTRUCTION   AND   DRAWING. 


310 


No.  4  IB  from  a  plain  slide  valve  engine,  18  inches  bore  and  3 
ft.  stroke,  of  good  construction  and  apparently  in  good  order. 
It  shows  but  55.33  per  cent,  of  the  theoretical  diagram.  It  will 
be  noticed  in  this  case,  that  the  theoretical  compression  curve 


does  not  touch  the  actual  line,  except  at  the  point  of  the  pecu- 
liar hook,  which  is  probably  owing  to  a  leakage  of  the  piston. 

No.  5  is  from  an  engine  of  23  inches  bore  and  4  ft.  stroke. 
It  figures  7H  per  cent,  of  the  theoretical  diagram. 


320  ELEMENTS   OF 

No.  6  was  taken  from  a  condensing  steam  engine,  fitted  with 
poppet  valves,  actuated  by  toes,  and  shows  71f  pe.r  cent,  of  the 
theoretical  effect. 


EXAMPLE  LXV. 
The  Putnam  Machine  Go's   Variable  Cut-off. 

Description.— ?\.  XVI.,  Figs.  11,  12.  Let  the  observer  be 
supposed  to  be  facing  the  front  end  of  the  cylinder  of  a  hori- 
zontal engine,  with  the  steam  chest  on  what  will  then  be  the 
right  hand  side  of  the  cylinder.  In  this  chest  are  the  poppet 
valves  opening  upward  ;  and  the  parts  shown  in  the  figure  will 
be  under  the  steam  chest. 

A  is  a  section  of  the  cam  shaft,  moved  by  gearing  on  the 
main  shaft,  and  lying  parallel  to  the  cylinder. 

The  manner  of  lifting  the  valves  is  designed  to  overc-<  >me  all 
shock  in  their  rising  and  falling.  The  actual  construction  va- 
ries somewhat,  but  the  principle  is  shown  in  the  figure.  The 
cam  shaft,  in  this  case,  has  the  same  angular  velocity  as  the  en- 
gine shaft,  and  when  connected  as  shown  in  Fig.  11,  is  adapted 
for  large  engines.  The  auxiliary  lever,  D,  has  a  horizontal  and 
vertical  motion,  the  corner,  7,  describing  nearly  a  semicircle 
and  returning  on  the  diameter,  operating  against  the  lever,  B,  to 
raise  the  valve,  the  position  of  the  fulcrum  of  B  being  under 
control  of  the  governor.  The  rise  and  fall  of  the  governor 
spindle  oscillates  the  lever,  F,  by  means  of  an  arm,  keyed  to  H, 
or  in  any  convenient  manner ;  and  thus  determines  when  the 


MACHINE  CONSTRUCTION  AND  DRAWING. 


321 


corner,  7,  shall  pass  the  corner  8,  and  thus  let  go  of  the  valve  ; 
which  will  then  drop  to  its  seat.  The  lever  as  in  Fig.  11,  is 
operated  by  a  double  cam — GE,  Fig.  12 — the  part  c  of  the 
lever  rests  upon  the  G  part  of  the  cam,  during  the  entire  revo- 
lution, while  the  lever  receives  horizontal  motion  from  the  ec- 
centric E,  acting  against  the  straight  sides,  mn,  of  the  opening 
of  the  lever  within  which  it  plays.  It  will  be  observed  that  the 
corner,  7,  never  falls  below  the  under  side  of  the  lever  B,  but 
slides  along  in  contact  with  it. 


• 


EXAMPLE  LXTL 
The  Eider  Cut-off. 

Description. — Fig.  112  clearly  illustrates  this  novel  and  sim- 
ple variable  cut-off,  with  the  valve  chest  removed.     The  rise 
and  fall  of  the  governor  spindle  is  made  to  rotate  the  obliquely 
21 


322  ELEMENTS   OF 

truncated  half-cylindrical  cut-off  valve,  CO,  and  its  stem,  T,  by 
means  of  an  arm  from  T  ;  or  a  toothed  sector,  gearing  with  a 
rack,  formed  by  teeth  on  the  lower  end  of  the  governor  spindle. 
The  angular  position  of  the  valve  thus  determines  the  time  of 
cutting  off  steam  from  the  oblique  ports,  seen  in  the  main  slide 
valve.  These  ports  pass  spirally  through  the  valve,  SS,  so  that 
on  its  plane  under  side  they  are  rectangular  and  perpendicular 
to  the  axis  of  the  steam  cylinder  in  the  usual  way. 

Construction. — After  the  practice  from  measurements,  which 
the  student  has  thus  far  had,  it  will  be  sufficient  to  assume  them 
for  this  example.  As  a  key  to  the  relative  position  of  the  piston 
and  the  two  valves,  in  making  a  section  as  in  PI.  IY.,  Fig.  1,  note 
that  when  the  piston  is  at  either  end  of  its  stroke,  the  main  valve, 
having  no  lap,  is  exactly  at  midstroke,  except  by  the  amount  of 
the  lead ;  and  the  cut-off  valve  is  in  a  position  to  have  the  port 
on  top  of  the  main  valve  wide  open.  Also,  the  main  valve  hav- 
ing no  lap,  its  travel  need  be  but  twice  the  width  of  its  steam 
port. 

The  following  more  definite  data  from  a  model,  will  serve  as 
well  as  if  from  actual  practice,  for  the  purpose  of  locating  the 
eccentrics,  and  thence  the  position  of  both  valves,  for  any  piston 
position.  They  are  all  in  GOths  of  an  inch. 

Stroke  of  piston  =  168.  Width  of  steam  ports,  8|.   Do.  over  all  the  ports,  43. 

Travel  of  main  valve,  constant  =  17,  =  8£  each  way  from  midstroke. 
"        "  cut-off  "  "        =  21,  =  10£       "  "  " 

"        "  cut-off  "  on  main  valve  13,  =  6£         "      of  centre  of  cut-off  from 
centre  of  main  valve. 

These  half  travels,  8|-  and  10|,  give  the  throws  of  the  eccen- 
trics ;  and  then  the  last  item  will  show  what  angle  they  should 
make  with  each  other. 


EXAMPLE  LXYIL 
Sibley  and  Walsh's  Water-  Wheel  Governor. 

Description.  PL  XXXIV.,  and  Fig.  114.  In  the  plate,  Fig. 
1  represents  a  sectional  elevation  of  the  governor.  Fig.  2  is  a 
sectional  plan,  on  the  plane  xx.  Fig.  3  shows  a  separate  view 
of  the  stop-plate  which  operates  to  detach  the  pawls,  LI/. 

Like  letters  indicate  like  parts  on  all  the  figures.  A  is  the 
bed.  B  is  the  frame.  C  is  the  governor  head.  D,  the  governor 


MACHINE   CONSTRUCTION  AND   DRAWING.  323 

balls,  and  E,  the  governor  spindle.  F  is  a  band  pulley,  by  which 
the  governor  is  rotated  through  the  action  of  the  bevel  gears, 
G  and  H,  as  shown  on  Fig.  114.  I  is  a  frame — or  bar,  Fig. 
114 — sliding  on  the  bed,  and  moved  by  the  eccentric,  J,  on  the 
spindle,  E,  by  means  of  the  rod,  K. 

This  frame,  I,  is  provided  with  four  pawls,  LL' — two  only  in 
Fig.  114 — which  engage  with  the  ratchet  wheel,  M,  through  the 
reciprocating  motion  of  the  frame,  or  bar,  I.  The  pawls  LL 
turn  the  wheel  M  in  one  direction,  and  the  pawls  L'L'  turn  it  in 
the  opposite  direction ;  but  they  engage  with  M  only  when 
there  is  a  variation  in  the  speed  of  the  governor.  N  is  a  shield 
on  the  shaft,  or  spindle,  O,  to  which  shaft  the  ratchet  M  is 
attached. 

The  shield  N  extends  in  the  form  of  guard-plates,  P — the 
concentric  shell  segment,  M',  in  Fig.  114 — which  so  cover  some 
of  the  teeth  of  M,  as  to  prevent  the  pawls  from  engaging  with 
M,  except  when  opening  or  closing  the  water-wheel  gate  by  the 
action  of  the  bevel  gears,  Q,  Fig.  114.  The  positions  of  N*and 
P  are  controlled  by  the  governor. 

The  vertical  motion  of  the  governor  spindle,  E,  is  transmitted 
by  the  grooved  thimble,  R,  through  the  forked  bell-crank,  S, 
oscillating  on  the  shaft,  T,  and  through  the  rod,  U,  to  the  shield 
N ;  which  is  thus  made  to  oscillate  on  the  shaft  O,  and  to  vary 
the  position  of  the  guards,  P. 

The  pawls  are  kept  in  contact  with  the  guards,  when  not  engaged 
with  M,  by  means  of  the  small  springs,  V,  attached  to  the  studs, 
W,  as  shown.  X  is  the  stop,  which  consists  of  a  bar  in  which  the 
shaft,  O,  works  by  a  screw  thread,  so  that  the  rotation  of  O 
carries  X  in  the  direction  of  the  length  of  O. 

As  the  wheel  M  is  turned,  X  will  finally  be  brought  to  the 
shoulder  on  the  screw-shaft,  O ;  and  then  the  water  gate  will  be 
fully  open,  and  the  stop,  X,  will  turn  with  the  wheel  M  ;  its 
motion  being  limited,  however,  by  the  stud  X'.  The  pin,  y,  in 
the  bar,  X,  will  be  in  contact  with  the  pin,  z,  in  the  shield  N, 
and  will  hold  the  latter,  with  the  guards,  P,  in  such  a  position 
as  to  prevent  the  pawls,  L,  L',  from  engaging  with  M.  At  the 
same  time,  the  governor,  by  the  action  of  its  varied  velocity 
in  putting  the  guards,  P,  out  of  the  way  of  the  pawls,  LL',  is 
left  free  to  close  the  water  gate  as  may  be  required. 

Fig.  3,  «',  shows  a  plate  which  turns  on  the  shaft  O,  and,  by 
means  of  the  rod,  I',  may  be  made  to  disengage  the  pawls  from  the 


324  ELEMENTS   OF 

ratchet  wheel  M,  when  it  is  desired  to  close  the  gate  by  the  hand 
wheel  Y.  The  plate,  O,  is  recessed  as  at  a' a',  to  allow  the  pawls 
to  engage  with  M  at  other  times. 


Fia.  114. 


The  wheel  M  may  be  horizontal,  as  in  the  plate,  or  vertical, 
as  in  Fig.  114,  and  with  two  or  four  pawls. 

Operation. — When  the  water-wheel  revolves  too  slowly,  the 
balls  fall,  E  rises,  S  swings  to  the  right,  L'  is  let  into  the  teeth 
of  M,  and  turns  it  as  I  makes  its  stroke  to  the  left,  so  as  to 
open  the  gate. 

When  the  water-wheel  revolves  too  fast,  the  balls  rise,  E 
falls,  S  swings  to  the  left,  L  is  engaged  with  the  teeth  of  M 
and  actuates  it  during  the  stroke  of  I  to  the  right,  so  as  to  close 
the  gate ;  I  being  constantly  actuated  back  and  forth  by  the 
eccentric  J. 

Construction. — These  governors  are  made  of  various  sizes,  and 
of  partly  different  proportions,  to  suit  different  cases.  A  scale 


MACHINE   CONSTRUCTION   AND   DRAWING.  325 

for  PI.  XXXIY.  can  be  determined  by  assuming  the  balls  D  tc 
be  four  inches  in  diameter. 

"With  a  little  care,  especially  where  an  example  of  the  gover- 
nor is  accessible,  Fig.  114  can  be  transformed  into  plans  and 
elevations.  Also  an  end  elevation  could  be  added  to  PI. 
XXXIV.  In  the  elevation  the  top  of  the  bed,  A,  and  the 
centre  lines  of  E  and  O,  will  be  convenient  lines  of  reference 
to  work  from  ;  and  in  the  plan,  a  line  joining  the  centres  of  O 
and  E  will  be  a  useful  line  of  reference. 


MODULATORS. 

EXAMPLE  LXYIII. 

Com/pound  Speed  and  Feed  Motions. 

Among  compound  modulators  forming  trains  of  mechanism, 
feed  motions  may  first  be  mentioned. 

The  utmost  number  of  plates  being  now  full,  the  skeleton, 
Fig.  115,  may  represent,  in  plan,  the  feed  movement  of  a  grand 
shaping  machine  by  the  celebrated  Joseph  Whitworth,  of  Man- 
chester, Eng.,  for  finishing  up  propeller  blades.  F  is  a  tapering 
" mandril"  so  made  for  the  purpose  of  taking  up  all  wear,  by 
slipping  it  further  into  its  bearings,  so  that  it  will  revolve  with- 
out play  in  its  bearings,  or  journals,  at  F  and  F ;  whose  massive 
common  support  is  called  a  headstock.  FL  is  the  radius  of  the 
circular  face-plate,  the  many  rectangular  holes  in  which  allow 
work  to  be  clamped  to  it  in  any  position.  FM,  FN,  and  FO  are 
three  concentric  spur-toothed  rings,  bolted  to  the  back  of  the 
face-plate,  to  allow  it-to  be  driven  at  various  speeds.  P  is  the 
band  pulley,  from  which  all  parts  take  motion,  and  which  may 
be  attached  to  either  of  the  other  speed  shafts,  1,  2,  or  3.  The 
spur  wheel,  R,  sliding  by  a  feather  in  a  longitudinal  groove  in 
the  shaft  P^,  may  thus  be  in  or  out  of  gear  with  the  spur-wheel 
S,  on  the  shaft  1 ;  which,  by  a  pinion,  b,  at  M,  carries  the  face- 
plate. Pinion  T  is  on  the  same  hub,  or  "  boss,"  with  S,  and  is 
in  gear  with  U  on  shaft  2.  Now  U  can  be  put  in  gear  with 


326 


ELEMENTS   OF 


pinion  V,  on  shaft  3,  carrying  the  pinion  X,  to  gear  with  O  for 
driving  the  face-plate  at  its  quickest  speed.  Shaft  2,  carrying 
wheel  Y,  has  also  upon  it  a  pinion  Y,  in  gear  with  wheel  Z,  on 
shaft  1.  The  pinion  #,  gearing  with  N,  gives  the  intermediate 
face-plate  speed,  and  pinion  I  on  shaft  1,  acting  with  ring  FM 


Fia.  115. 


gives  the  slowest  speed.  The  shaft  ~Pg  is  supported  by  interme- 
diate bearings,  as  <?,  and  one  on  the  standard /|  where  it  carries 
the  spur-wheel,  g,  which  gears  into  A,  which  turns  loosely  on  a 


MACHINE  CONSTRUCTION  AND  DRAWING.  327 

fixed  stud  h',  and  gears  with  i  on  the  screw  shaft  j.  At  m  ra, 
are  guides,  on  which  slides  the  great  slide  rest  n,  by  the  work- 
ing of  the  revolving  screwy',  in  the  long  fixed  nut  o,  on  the 
under  side  of  n. 

This  part  of  the  movement  advances  the  tool,  t,  against  the 
propeller  blade  B,  according  to  the  pitch  of  the  latter,  as  the 
face-plate  revolves. 

Again:  a  bevel  pinion p'  with  a  long  feathered  boss,  on  P$>, 
revolving  with  P<7,  moves  another  pinion  j?,  on  the  axis  of  which 
is  r,  gearing  with  s,  loose  on  a  stud,  and  so  driving  a  larger 
wheel,  c,  not  shown,  on  the  screw  shaft,  u,  which,  by  working 
through  the  slide  v,  gives  transverse  motion  to  the  tool,  to  enable 
it  to  make  its  concentric  parings  from  the  blade  B. 

Wheel  q,  by  gearing  with  a  pinion  on  the  shaft  of  £,  then  put 
in  gear  with  c,  will  give  a  quicker  transverse  feed. 

Various  sets  of  the  wheels  g,  A,  and  *,  provide  for  different 
pitches  of  the  screw  to  be  trimmed. 

Construction. — This  example,  by  the  very  rude  illustration 
given  of  it,  may  serve,  more  fully  than  any  previous  one,  as 
one  in  mechanical  design. 


EXAMPLE  LXIX. 
WhitwortKs  Quick  Return  Motion. 

Description. — Quick  return  motions  are  contrivances  for  with- 
drawing a  tool  across  the  surface  of  its  work  for  a  new  cut, 
faster  than  it  works  in  making  a  cut,  so  as  to  save  a  part  of  the 
time  in  which  it  is  idle. 

PL  XXXI.,  Fig.  11,  shows  a  very  ingenious  and  admired 
form  of  quick  return,  Af or  a  shaping  machine  ;  that  is,  a  planing 
machine  for  irregular,  or  curved  work.  An  arm  at  A,  takes 
hold  of  the  stock,  which  carries  the  cutting  tool,  and  leads  it 
back  and  forth,  as  actuated  by  the  connecting-rod,  G,  proceed- 
ing from  the  crank-pin,  H  ;  whose  distance  from  the  fixed 
centre  of  motion,  O,  is  adjustable.  H  is  clamped  in  the  radial 
groove  of  the  crank  piece,  I,  which  is  carried  by  the  spur-wheel 
J,  which  revolves  in  the  very  stout  bearings  K&.  This  being 
hollow,  as  shown  by  the  dotted  circles,  K  and  &,  the  spindle,  C, 
of  the  crank  piece,  I,  passes  through  it.  There  is  a  radial  slot 


328 


ELEMENTS   OF 


in  that  side  of  I  which  rests  against  J,  and  in  the  contiguous 
side  of  the  wheel  J  is  a  pin,  L,  carried  in  the  square  bush  D, 
which  slides  in  this  slot.  The  pin,  L,  with  its  bush,  D,  imparts 
the  motion  of  J  to  I.  Now  LO  is  a  fixed  distance,  and  so  is  CO, 
but  LC  is  variable,  being  now  =  LO  —  CO ;  but  when  L  is  on 
the  opposite  side  of  O,  we  shall  have  LC  =  LO  +  OC.  And 
this  variable  distance  of  L,  from  the  centre  of  motion,  C,  of  the 
crank,  makes  the  return  motion,  in  the  sense  of  the  arrow,  quick, 
and  the  advance  motion,  when  LC  =  LO  +  OC  slow. 

Construction. — This  example  may  well  be  drawn  twice  as 
large  as  in  the  figure. 


EXAMPLE  LXX. 
Mason's  Friction  Pulleys  and 


'8  or   Clutches. 


Description. — In  the  above  cut,  the  friction  pulley  shown, 
consists  of  the  two  main  parts,  the  loose  pulley  B,  and  the  shaft 


MACHINE   CONSTRUCTION   AND  DEAWING.  329 

A,  on  which  is  keyed  the  part  second,  which  consists  of  a  plate 
or  disk,  D,  and  two  segments,  EE,  and  the  sliding  sleeve  or 
thimble,  F.  The  two  segments,  EE,  are  fitted  to  slide  radially 
on  the  face  of  the  disk,  between  ribs  or  guides,  cast  on  the 
plate  DD,  and  are  operated  by  means  of  the  adjustable  toggle 
joints  shown.  It  will  be  seen  that  when  the  thimble,  F,  is 
moved  towards  the  plate,  the  segments  EE  are  forced  outwards 
in  contact  with  the  inside  of  the  pulley  A,  thereby  producing 
friction  between  the  two  surfaces  sufficient  to  drive  the  ma- 
chinery to  which  it  is  applied.  The  ball  and  socket  joint  used, 
is  more  plainly  seen  in  the  figures  117  and  119  of  the  friction 
coupling,  shown  by  the  letters  e,f,  and  g. 

Belts  running  over  the  friction  pulleys  will  run  much  longer 
without  necessity  of  tightening,  than  when  they  are  constantly 
shipped  from  one  pulley  to  another. 

In  some  cases  friction  pulleys  may  be  placed  on  the  main  line 
and  used  to  stop  and  start  machines  driven  directly  from  the 
main  line. 


Method  of  Adjusting  the  Friction. 

The  friction  pressure  may  be  nicely  adjusted,  by  placing  the 
centres  of  the  segments  in  a  horizontal  position,  and  then  tak- 
ing two  strips  of  stiff  paper,  and  placing  one  strip  between  the 
centre  of  each  segment  and  the  inside  of  the  pulley,  when  un- 
shipped, then  slowly  ship  the  thimble  towards  the  plate,  and 
note  which  strip  of  paper  tightens  first ;  the  adjustment  is  then 
easily  effected  by  screwing  the  connecting  arms  out  or  in  until 
the  pressure  is  alike  on  each  segment,  and  sufficient  to  drive 
without  slipping ;  then  tighten  the  check-nuts,  FF,  firmly 
against  the  joint  to  prevent  the  screw  from  loosening.  Care 
should  be  taken  not  to  set  out  too  hard,  so  as  not  to  prevent  the 
thimble  from  always  shipping  up  closely  against  the  plate,  as 
the  joints  are  so  arranged  that  the  centres  of  the  joints  of  the 
thimble  will  just  pass  by  a  line  drawn  through  the  centres  of 
the  joints  of  the  segments,  thereby  holding  itself  in  when  the 
thimble  is  fully  shipped  up  against  the  plate. 

This  adjustment  should  always  be  attended  to  by  a  good 
mechanic,  on  the  first  starting  up,  as  when  properly  adjusted 
they  will  generally  run  one  and  two  years,  and  often  longer, 
without  any  readjusting. 


330 


ELEMENTS   OF 


Fio.   117.— Thirty-six  inch  Friction  Coupling,  one-twelfth  size. 

Figure  117  represents  a  view  of  the  friction  coupling  as  ap- 
plied for  connecting  shafting.  The  shafts  A  and  B,  are  made 
one  to  enter  the  other,  so  as  to  help  keep  them  in  line  ;  some- 
times it  is  more  convenient  to  drill  into  the  end  of  each  shaft, 
and  put  in  a  steel  pin,  instead  of  letting  one  shaft  enter  the 


MACHINE   CONSTRUCTION  AND   DRAWING.  331 

other.  The  segments  of  this  friction  coupling,  have  a  V,  or 
wedge  form,  by  which  a  very  powerful  friction  is  produced,  for 
connecting  heavy  shafting  and  gearing. 


Fig.  118  shows  the  slides  or  ribs  on  the  plate,  also,  the  ball 
joint  and  screw  and  check  nuts,  and  T  joints  of  the  thimble,  in 
their  relative  positions. 


Fig.  119  shows  one  method  of  applying  the  friction  for  start- 
ing and  stopping  gears,  as  used  for  force  pumps,  grinding  mills 


332  ELEMENTS   OF 

and  other  machinery,  which  can  by  this  method  be  driven 
directly  from  the  main  shafting ;  stopping  both  gears  when 
the  friction  is  unshipped.  By  this  method,  there  is  no  danger 
of  breaking  the  gear  teeth  on  starting,  nor  any  necessity  for 
slacking  speed,  on  starting  any  machinery  which  they  may  be 
employed  to  drive ;  as,  in  case  of  sudden  unusual  strain  being 
brought  on  the  machine,  the  friction  may  be  so  adjusted  as  to 
slip  a  trifle,  thereby  saving  the  breaking  of  shafts  or  teeth  of 
gears.  In  cases  of  fires  in  factories,  force  pumps  have  fre- 
quently been  disabled  and  rendered  useless  by  the  breaking 
down  of  the  gears  or  shafts  ;  and,  in  places  where  frictions  are 
not  in  use,  it  is  necessary  to  stop  the  engine,  or  water  wheel, 
before  the  pump  gear  can  be  thrown  in ;  while  by  the  use  of 
friction,  any  force  pump  can  be  started  up  promptly  in  case  of 
fire,  without  stopping  or  hindering  the  motive  power. 

These  friction  clutches  are  also  very  useful  for  hoisting,  as  at 
coal,  copper  and  gold  mines,  and  in  tunnel  shafts  and  rolling 
mills,  and  have  been  furnished  for  use  at  a  number  of  different 
copper  mines  in  Chili,  South  America  and  elsewhere.  They  are 
applied  between  the  engine  and  large  winding  drum,  for  revers- 
ing the  motion  of  the  drum,  which  fchey  accomplish  in  the  most 
perfect  manner.  Among  the  largest  yet  made  are  two  em- 
ployed to  reverse  the  motion  of  heavy  rolls  for  rolling  sheet 
lead.  The  two  weighed  about  five  thousand  eight  hundred 
pounds,  yet  are  light  in  comparison  with  the  ponderous  gears  to 
which  they  are  applied.  By  simply  working  the  lever  the  power 
is  arrested  or  transmitted  in  either  direction  almost  instanta- 
neously, without  any  shock  or  noise,  or  slacking  speed  of  engine. 
They  transmit  sixty  horse  power,  and  are  shipped  probably  two 
hundred  times  daily. 


EXAMPLE  LXXI. 
Reversing  Gear  for  the  Compound  Rolling-Mitt  Engine. 

Description. — PL  XI.,  Fig.  2.  In  this  figure,  the  plan  was 
improvised  from  a  given  elevation,  only,  but  will  answer  to 
illustrate  the  character  of  the  movement,  and  as  a  basis,  from 
which  the  student  can  proceed  to  make  modifications. 

SS'  is  the  main   shaft,  on   which  is  mounted,  loosely,  the 


MACHINE  CONSTRUCTION  AND  DRAWING.  333 

eccentric,  EE',  solid  with  the  bevel  wheel,  GG' ;  the  collar, 
CO',  and  the  sleeve,  AA',  which  slides  on  the  long  feather ff. 
CO'  and  AA'  revolve  with  the  shaft,  by  reason  of  the  feather, 
and  EG'— -E'G'  revolves  by  reason  of  the  hold  which  the  teeth 
of  the  bevel  sectors  LI/  and  FF'  have  upon  GG'. 

To  reverse  the  engine,  it  is  only  necessary  to  revolve  the  com- 
mon eccentric,  EE',  of  the  three  valves,  upon  the  shaft.  For 
this  purpose,  RR,'  is  a  loose  ring  on  the  sleeve,  AA'.  By  operat- 
ing a  handle  which  proceeds  from  it,  either  by  hand,  or  by 
power,  AA'  is  shifted  to  the  right  or  left,  and  thence  the  arms, 
««',  and  W,  rotate  the  bevel  sectors,  which  will  rotate  GG'  as 
desired.  These  arms  are  centred  on  the  studs,  ccf,  and  dd',  on 
the  sleeve,  and  the  sectors  are  centred  at  gg  on  studs  on  the 
collar  CO'. 

Construction.—  Let  this  figure  be  made  on  a  scale  of  one- 
twelfth,  and  with  the  sectors  in  some  ether  relative  position,  so 
that  the  arms  aa'  and  W  will  not  be  parallel.  Also  some  at 
least,  of  the  teeth  on  the  sectors  can  be  added,  and  an  end  view 
made. 


Escapements. 

233.  Escapements  are  of  comparatively  small  immediate  in- 
terest to  the  civil  or  mechanical  engineer,  as  such;  but  are 
intrinsically  attractive,  on  account  of  the  refined  ingenuity  of 
their  design,  and  by  association  with  astronomical  clocks  ;  cer- 
tain uses  of  which  in  engineering  practical  astronomy,  the  engi- 
neer should  be  acquainted  with.  Escapements  are  also  indi- 
rectly interesting  to  the  engineer  as  forming  a  part  of  some  of 
the  dividing  engines,  by  which  the  degree  circles  of  his  field 
instruments  are  graduated. 

Escapements  are,  finally,  interesting  as  being  the  only  means 
within  the  range  of  pure  mechanism,  that  is  by  motion  only, 
without  employing  inertia  as  in  case  of  a  fly-wheel  carrying  a 
crank  over  its  "  centre,"  for  converting  rotary  into  reciprocating 
motion. 

A  few  examples  therefore  are  here  given ;  as  a  proper  con- 
clusion of  this  work,  with  the  most  refined  constructions  that 
can  be  found. 


334  ELEMENTS   OF 

EXAMPLE  LXXII. 

JBoncTs  Escapement^  2fb.  2. 

Description. — What  follows  is  in  the  words  of  the  inventol 
and  makers. 

"  In  giving  the  description  of  my  Isodynamic  Escapement; 
No.  2,  it  will  be  necessary,  in  order  to  explain  its  advantages 
fully,  to  give  some  account  of  those  now  in  use,  and  of  the  ob- 
stacles still  remaining  to  be  overcome  in  order  to  obtain  one 
that  is  perfectly  exact. 

"  The  advantages  to  be  derived  from  the  possession  of  a  clock 
of  perfect  accuracy  (were  such  a  thing  possible),  could  hardly  be 
over-estimated.  The  science  of  astronomy,  in  particular,  would 
receive  important  benefit  from  such  an  instrument.  But  as  no 
timekeeper  has  ever  yet  been  constructed  that  could  be  relied 
upon  as  being  absolutely  free  from  error,  it  is  evident  that  there 
is  still  room  for  improvement.  The  sources  of  irregularity 
have  long  engaged  the  attention  of  many  able  scientific  investi- 
gators, and  very  numerous  contrivances  for  counteracting  them 
have  been  suggested.  These  remarks  refer,  of  course,  only  to 
such  timekeepers  as  have  the  pendulum  for  their  regulator,  and 
indeed,  no  other  natural  principle  is  practically  so  well  adapted 
to  produce  regularity. 

"  The  end  to  be  attained  is,  to  keep  the  pendulum  vibrating  al- 
ways in  the  same  arc,  always  encountering  the  same  amount  of 
resistance,  and  of  motive  power. 

"  The  principal  errors  may  be  divided  into  two  classes,  those 
arising  from  the  mechanical  intervention  necessary  to  maintain 
the  vibratory  motion  of  the  pendulum,  and  those  arising  from 
such  causes  as  would  still  affect  it,  provided  its  vibration  could 
be  maintained  by  a  uniform  force ;  for  instance,  changes  of 
the  themometer,  barometer  and  hygrometer,  magnetic  influen- 
ces, and,  to  a  slight  degree,  the  position  of  the  moon.  By  far 
the  most  important  of  these  errors  are  those  arising  from  the 
friction  influencing  the  pendulum  through  the  escapement,  as 
they  are  of  such  a  nature  as  renders  it  almost  impossible  to 
ascertain  beforehand  what  their  influence  will  be,  while  the 
residuary  errors  of  the  second  class  are  not  only  smaller  in 
amount,  but  can,  by  close  and  accurate  observation,  be  tabulated 


MACHINE   CONSTRUCTION   AND   DRAWING.  335 

and  the  corrections  applied.  It  is  the  first  class,  therefore,  of 
these  errors,  that  it  is  most  important  to  remedy,  and  the  power 
of  doing  this  lies  almost  entirely  in  diminishing,  or  equalizing 
the  friction  of  the  escapement.  The  mere  diminishing  of  the 
friction  is  not  the  only,  or  even  the  principal  desideratum  in 
such  improvement ;  the  equalizing  of  the  force  is  of  far  more 
consequence,  as  is  sufficiently  proved  by  the  single  instance  of 
the  deservedly  high  position  which  Graham's  escapement  has 
so  long  maintained,  notwithstanding  the  great  amount  of  fric- 
tion which  it  involves.  One  reason  of  its  superiority  to  many 
others  which  boast  far  less  actual  friction,  is  its  principle  of 
compensating  a  slightly  varying  power  upon  the  pallets,  by  a 
corresponding  variation  in  the  arc  described  by  the  pendulum  ; 
this  has  given  it  its  practical  utility.  This  escapement,  though 
invented  nearly  a  century  ago,  met  with  no  successful  rival, 
until  within  a  few  years.  It  has,  however,  recently  been  re- 
placed, in  some  astronomical  clocks,  by  Denison's  three-legged 
gravity  escapement.  The  superiority  of  this  latter  consists  in 
the  impulse  to  the  pendulum  being  given  either  by  the  force  of 
gravity,  influenced  by  a  small  amount  of  friction,  or  by  the 
force  of  a  spring  without  such  friction ;  but  in  either  case  there 
is  a  certain  amount  of  variable  resistance,  increasing  or  dimin- 
ishing as  the  wheel- work  of  the  clock  carries  more  or  less  power 
to  the  escapement,  and  consequently,  if  a  heavier  driving 
weight  is  applied,  the  pendulum  encounters  more  friction  in 
unlocking  the  escapement,  without  gaining  any  additional  im- 
pulse, as  it  wOuld  in  the  case  of  Graham's.  The  vibration  of 
the  pendulum  is  thus  affected,  and  its  rate  changed,  by  a  vary- 
ing cause,  dependent  upon  the  freedom  with  which  the  wheel- 
work  transmits  the  power,  and  which  it  is  impossible  to  calcu- 
late. Notwithstanding  this  defect,  this  method  has,  upon  the 
whole,  smaller  causes  of  error  than  any  hitherto  known. 

"  The  Isodynamic  Escapement,  recently  invented,  overcomes 
entirely  the  difficulty  of  the  varying  power  transmitted  by  the 
wheel  work,  and  thus  obviates  most  of  the  objections  to  other 
escapements.  In  comparing  it  with  previous  ones,  I  refer  only 
to  Denison's  and  Graham's,  they  combining  to  a  greater  degree 
than  any  others  the  various  requisites  essential  to  a  good  escape- 
ment. 

"  Besides  the  difficulties  already  enumerated,  which  are  to  be 
overcome  in  making  a  perfectly  reliable  gravity  escapement, 


336  ELEMENTS   OF 

there  is  one  which  has  been  exceedingly  troublesome,  namely, 
the  necessity  of  guarding  against  what  is  called  tripping,  or  the 
danger  of  two  or  more  teeth  of  the  escapement  wheel  passing 
the  pallets  at  once,  when  one  only  is  intended  to  do  so.  This 
causes  the  hand  of  the  clock  to  gain  by  jumps,  and  of  course, 
in  a  most  unreliable  manner,  while  the  pendulum  may  be 
vibrating  with  perfect  regularity.  Mr.  Denison,  in  his  book  on 
'  Clock  and  Watch  Work,'  speaks  of  guarding  against  this  diffi- 
culty as  first  among  the  essential  mechanical  conditions.  Even 
in  his  own  gravity  escapement,  to  which  I  have  already  referred, 
the  possibility  of  tripping  still  exists,  though  rendered  reasona- 
bly slight  by  the  introduction  of  a  fan  upon  the  escapement 
wheel,  but  in  the  Isodynamic  Escapement,  it  will  be  seen  that 
this  danger  is  completely  removed." 

The  escapement,  of  which  PI.  XXXIII.,  Fig.  2,  is  a  draw- 
ing, is  of  the  class  known  as  gravity  escapements,  and  has  proved 
thoroughly  good  and  given  extremely  good  results.  The  ex- 
treme variation  in  the  hourly  rates  of  a  clock  with  this  escape- 
ment, for  a  considerable  length  of  time,  was  only  Os.020. 

In  the  figure,  g  and  g,  are  the  gravity  arms  hung  on  delicate 
pivots  at  a,p  and^/  the  pall ets,y  and  f  friction  rollers.  P  the 
pendulum,  and  S  the  scape  wheel,  revolving  five  times  a 
minute,  having  six  arms,  and  six  pins  d  d"  projecting  from  the 
face,  to  act  011  the  friction  rollers,/-/'.  At  the  moment  shown 
in  the  figure,  the  pendulum  has  completed  its  swing  to  the  left, 
and  has  just  began  to  move  to  the  right,  the  gravity  arm,  g,  be- 
ing in  contact  with  it,  and  assisting  the  vibration  "by  its  weight, 
until  the  adjusting  screw,  J,  comes  in  contact  with  the  stop,  c. 
The  gravity  arm,  g',  has  in  the  mean  time  been  raised  slightly 
by  the  pin  d'  in  the  scape  wheel,  coming  in  contact  with  the 
friction  roller,  /',  and  the  arm,  ra',  of  scape  wheel  has  locked  on 
pallet,  p'.  As  the  pendulum  continues  to  move  to  the  right,  it 
comes  in  contact  with  adjusting  screw  n',  and  carries  gravity 
arm  g',  with  it,  to  the  right.  This  unlocks  the  arm  ml ',  the 
scape  wheel  moves  forward  until  the  pin  d'  comes  in  contact 
with  friction  roller,/,  raises  it  a  little,  and  arm,  ra,  locks  on 
pallet  p,  until  it  is  again  unlocked.  It  will  be  seen  from  this, 
that  the  impulse  is  constant,  being  the  weight  of  the  gravity 
arm,  acting  on  the  pendulum  through  the  distance  it  is  raised 
by  the  pin  in  the  scape  wheel,  since  it  falls  back  in  contact 


MACHINE   CONSTRUCTION   AND   DRAWING.  337 

with  the  pendulum  that  much  more  than  the  distance  through 
which  the  pendulum  has  raised  it. 


EXAMPLE  LXXIII. 
Bond's  Auxiliary  Pendulum  Gravity  Escapement. 

Description. — This  again  is  nearly  in  the  words  of  the 
makers.  PI.  XXXIII.,  Fig.  3.  This  was  the  last  invention  of 
the  artist,  Mr.  Richard  F.  Bond,  perfected  indeed  on  the 
morning  of  his  death.  Its  mechanical  beauty  is  shown  even 
more  clearly  in  the  drawing,  than  it  appears  in  the  clock,  where 
it  is  necessarily  somewhat  confused  with  the  other  details. 

It  is  an  entirely  new  escapement,  nothing  like  it  ever  having 
been  made  before,  and  with  the  exception  of  the  Remontoir 
clocks,  which  are  entirely  different  in  principle,  this  is  the  first 
clock  which  has  ever  been  made,  with  &  perfectly  detached  es- 
capement. The  border  of  the  plate  represents  the  back  plate 
of  the  clock,  and  all  the  work  shown  is  on  the  outside  of  this 
plate.  The  wheel,  b,  is  in  connection  with  the  train  of  the 
clock,  and  is  constantly  revolving  with  a  uniform  velocity, 
making  one  revolution  in  little  less  than  one  second,  and  is  reg- 
ulated and  controlled  by  the  conical  pendulum,  not  shown  in 
the  drawing,  which  also  revolves  once  a  second. 

S  is  the  scape  wheel,  with  the  scape  arm,  «„  secured  firmly  to 
its  axis,  and  moving  freely  on  delicate  pivots,  working  in  pol- 
ished jewel  holes ;  or,  as  made  in  the  first  two  clocks,  sent  by 
the  makers  to  Paris  and  Liverpool,  the  pivots  of  the  scape 
wheel  worked  on  small  friction  rollers. 

The  scape  wheel,  #,  gears  in  with  the  constantly  moving  wheel 
b  /  but,  at  the  moment  shown  in  the  drawing,  it  is  entirely  detached, 
a  few  teeth  being  omitted  in  the  scape  wheel,  so  that  when  the 
arm  #„  locks  on  the  pallet,  p,  in  the  gravity  arm  g,  it  rests  there 
merely  by  its  own  weight,  the  wheel  b  continues  to  revolve,  but 
the  scape  wheel  8  remains  at  rest.  'There  is  also  a  jewelled 
cam,  e,  on  the  axis  of  the  scape  wheel,  which,  just  before  the 
arm  sl  locks  on  the  pallet^?,  comes  in  contact  with  the  friction 
roller/" on  the  gravity  arm,  thereby  raising  it  slightly,  in  order 
to  give  the  necessary  impulse  to  the  pendulum  P,  which  is  repre- 
sented as  moving  to  the  right.  At  the  lower  end  of  the  gravity 
22 


338  ELEMEOTS    OF    MACHETE   COXSTKUCTIOX. 

arm  is  the  screw  &,  which  carries  a  jewel  o  on  its  end,  and  as  the 
pendulum  comes  in  contact  with  it,  it  moves  the  gravity  arm 
also  to  the  right,  thereby  releasing  the  arm  *„  which  falls  by  its 
own  weight.  This  causes  the  wheels  s  and  b  to  gear  together 
again.  The  scape  wheel  is  caught  up  by  the  constantly  moving 
wheel,  I,  and  is  carried  over,  until  the  cam,  <?,  raises  the  gravity 
arm,  the  arm,  s',  locks  again  on  the  pallet  p,  and  the  scape  wheel, 
disengaged  from  wheel  b,  again  comes  to  rest.  There  is  also 
another  jewelled  cam  on  the  axis  of  the  scape  wheel,  which  at 
the  instant  that  arm  *,  drops  from  the  pallet  and  the  scape 
wheel  is  caught  up  by  wheel  b,  engages  with  a  tooth  of  wheel  c 
and  moves  it  forward  one  tooth.  The  axis  of  wheel  c  carries 
the  seconds  hand ;  and  a  pinion  on  the  same  arbor,  under  the 
dial,  in  connection  with  other  wheels  and  pinions,  moves  all  the 
hands  at  once.  M  is  a  stop  screw,  shaded  dark  behind  screw  k, 
which  regulates  the  movement  of  the  gravity  arm  to  the  left, 
and  so  adjusts  the  amount  of  impulse  which  the  pendulum  shall 
receive. 

It  will  therefore  be  seen  that  the  whole  timekeeping  part  of 
the  clock  consists  of  the  pendulum  P,  the  scape  wheel,  and 
arms  s  and  *„  and  the  gravity  arm,  g ;  the  scape  arm  falling 
from  the  pallet  p  at  regular  intervals  of  two  seconds,  measured 
by  the  vibrations  of  the  pendulum  P.  The  rest  of  the  clock 
may  therefore  be  regarded  as  an  auxiliary  machine,  to  carry  the 
scape  wheel  round  until  it  locks,  to  raise  the  gravity  arm,  and 
to  move  the  hands ;  all  heavy  work,  which  has  nothing  to  do 
with  the  time-keeping  qualities  of  the  clock,  and  it  might  be 
used  to  give  motion  to  any  number  of  instruments  or  machines, 
for  recording  meteorological  observations,  or  anything  else  that 
might  be  desired,  and  the  time  of  the  clock  would  not  be  in- 
fluenced in  the  slightest  degree. 

The  great  difficulty  to  be  overcome,  was  to  make  the  two 
wheels  b  and  s  gear  together  properly,  without  having  the  points 
of  the  teeth  jam  together,  which  would  stop  the  clock,  and  this 
was  effected  at  last  by  making  the  first  two  teeth  in  wheel  s 
movable,  they  pass  through  the  rim  of  the  wheel  as  shown,  and 
rest  on  delicate  springs  v  v,  which  yield  to  the  slightest  pressure 
and  permit  the  teeth  to  slip  into  their  proper  place. 


TJ 

530 

vt/3 


THE  LIBRARY 
NIVERSITY  OF  CALIFORNIA 

Santa  Barbara 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW. 


000  750  748 


